Mixed Multi-Step Word Problems Lesson Test

Answer: B

Correct answer: 185 minutes. Convert hours to minutes first:

Then add:

• A: Adding 2.25 and 50 directly combines hours and minutes without converting.
• B (correct): Converting 2.25 hours to 135 minutes and adding 50 minutes gives 185 minutes.
• C: This reads 0.25 hour as 25 minutes; a quarter hour is 15 minutes.
• D: This treats 2.25 hours as 225 minutes instead of multiplying by 60.

Answer: D

Correct answer: $273. The delivery charge applies to every chair, so each chair costs

delivered. For 7 chairs:

• A: This leaves out the delivery charges entirely.
• B: This adds the $4 delivery only once, but it is charged per chair.
• C: This is the delivered cost of a single chair, not the whole order.
• D (correct): Each chair costs $39 with its delivery charge, and 7 × $39 = $273.

Answer: B

Correct answer: $52.50. Only distance, mileage and price matter. Gallons used:

Cost:

The number of workers and the shift length are not needed.

• A: Multiplying the miles per gallon by the price does not give the fuel used on this trip.
• B (correct): The van uses 240 ÷ 16 = 15 gallons, and 15 × $3.50 = $52.50.
• C: Multiplying by the 3 workers uses a fact that has nothing to do with fuel use.
• D: Multiplying miles by the price per gallon skips converting miles to gallons.

Answer: C

Correct answer: 63. The ratio has

parts, so one part is

vehicles. Trucks:

• A: Dividing 99 by the difference of the parts (3) does not split the total into equal shares.
• B: This is the size of one ratio part, an intermediate value.
• C (correct): With 11 parts of 9 vehicles each, the trucks are 7 × 9 = 63.
• D: This is the number of sedans, the 4-part group.

Answer: A

Correct answer: 234. Interviewed:

Accepted:

The 65% applies to the 360 interviewed, not to all 840.

• A (correct): Sixty-five percent of the 360 interviewed applicants is 234.
• B: This is the number interviewed, a stepping stone rather than the final answer.
• C: This takes 65% of all 840 applicants instead of only those interviewed.
• D: This is the number interviewed but not accepted.

Answer: C

Correct answer: 1,269. Total made:

units. Defective:

units. Good units:

• A: This is the number of defective units, not the good ones.
• B: Subtracting 6 units instead of 6 percent of the total understates the defects.
• C (correct): The line makes 1,350 units, and removing the 81 defective ones leaves 1,269 good units.
• D: This is the total produced before removing the defective units.

Answer: C

Correct answer: 12:10 p.m. First leg:

Second leg:

Adding the 40-minute stop gives 5 hours 40 minutes, and 6:30 a.m. plus 5 hours 40 minutes is 12:10 p.m.

• A: Writing 40 minutes as 0.40 hour turns the stop into only 24 minutes.
• B: This counts both driving legs but leaves out the 40-minute stop.
• C (correct): Driving takes 3 + 2 = 5 hours, and with the 40-minute stop the trip lasts 5 hours 40 minutes, ending at 12:10 p.m.
• D: Averaging the two speeds to 60 mph gives the wrong driving time; each leg must be timed separately.

Answer: B

Correct answer: $607. Gravel:

Add the delivery fee once:

• A: This is the cost of one cubic yard plus the fee, not the whole order.
• B (correct): The gravel costs $532, and adding the single $75 fee gives $607.
• C: This is the cost of the gravel alone, without the delivery fee.
• D: This charges the $75 delivery fee for every cubic yard instead of once.

Answer: A

Correct answer: $45,000. The new salary is 1.08 times the old one, so divide:

Check: 8% of $45,000 is $3,600, and

• A (correct): Dividing $48,600 by 1.08 undoes the raise, and the check confirms it.
• B: This adds another 8% instead of undoing the raise.
• C: This is the dollar amount of the raise, not the original salary.
• D: This subtracts 8% of the new salary, but the raise was 8% of the old salary.

Answer: A

Correct answer: 6.5 days. Crew A finishes

in 2 days, so $\frac{3}{4}$ remains. Together they do

per day, so the rest takes

Total:

• A (correct): Crew A's 2 days plus the 4.5 days the two crews need for the remaining three-fourths gives 6.5 days.
• B: This is Crew A's time alone, ignoring the help from Crew B.
• C: This is only the time after Crew B joins; Crew A's first 2 days must be added.
• D: This is the time for the whole job with both crews from the start.

Answer: B

Correct answer: 558. Monday:

shipped, leaving 780. Tuesday:

shipped, leaving 468. Wednesday:

tires.

• A: This takes 2/5 of the original 1,200 on Tuesday instead of 2/5 of the 780 left.
• B (correct): After shipping 420 and then 312, 468 tires remain, and the delivery of 90 brings the total to 558.
• C: This is the count after Tuesday; the 90 tires received on Wednesday still need to be added.
• D: This is the number shipped on Tuesday, not the number in stock.

Answer: D

Correct answer: 90. The ratio has

parts, so one part is

Staff:

Remote staff:

staff members work in the office.

• A: This is the number of staff members who work remotely.
• B: This takes 60% of all 180 employees, but the percent applies only to the 150 staff members.
• C: Subtracting the remote staff from all 180 employees wrongly counts the managers as office staff.
• D (correct): There are 150 staff members, and the 60% who are not remote equals 90.

Answer: D

Correct answer: 39 mph. Times:

the stop is 0.75 hour, and

for 5 hours in all. Total distance is 195 miles.

• A: Dividing by 4.25 hours of driving leaves out the 45-minute stop, which the question includes.
• B: Writing 45 minutes as 0.45 hour undercounts the stop; 45 minutes is 0.75 hour.
• C: Averaging the two speeds ignores that the driver spends different amounts of time at each speed.
• D (correct): Total distance of 195 miles divided by total time of 5 hours, including the stop, gives 39 mph.

Answer: C

Correct answer: $318.34. Subtotal:

After the discount:

With tax:

Add shipping once:

• A: This is the taxed total before the $12 shipping charge is added.
• B: Netting 15% off and 6% tax into 9% off does not apply each step to the current amount.
• C (correct): The discounted order of $289 becomes $306.34 with tax, and one $12 shipping charge makes $318.34.
• D: This charges $12 shipping on each of the 8 helmets instead of once per order.

Answer: D

Correct answer: $120.00. Undo the steps in reverse order. Remove the tax:

Undo the discount:

Check:

• A: Adding a net 15% to the amount paid combines the percents and uses the wrong base.
• B: Adding 25% to the amount paid does not reverse a discount and a tax correctly.
• C: This undoes only the tax; it is the sale price before tax, not the original price.
• D (correct): Dividing by 1.05 and then by 0.80 reverses both steps, and running $120 forward gives $100.80.

Answer: C

Correct answer: 420. Monday: one-third of 840 is 280, leaving 560 cans.

Tuesday: 25% of 560 is 140, so

cans remain. The 25% applies to what was left, not to the starting 840.

• A: This is the number given away on Tuesday, an intermediate value rather than the cans remaining.
• B: This is the count after Monday only; the Tuesday step was skipped.
• C (correct): After Monday 560 cans are left, Tuesday removes 25% of 560 (140), and 560 − 140 = 420 cans remain.
• D: This applies the 25% to the original 840 cans instead of to the 560 cans left after Monday.

Answer: C

Correct answer: 450 pounds. Add the ratio parts:

One part is

Gravel is 3 parts:

• A: This is the sand (2 parts), not the gravel.
• B: This is the size of one part, which is the cement, not the gravel.
• C (correct): The ratio has 6 parts, each part is 150 pounds, and gravel is 3 parts, or 450 pounds.
• D: This uses only 5 parts (2 + 3) as the total, leaving the cement out of the part count.

Answer: B

Correct answer: 18 quarts. Convert to one unit before adding: 3 gallons × 4 = 12 quarts.

Then

• A: This adds 3 and 6 without converting gallons to quarts first.
• B (correct): Converting 3 gallons gives 12 quarts, and 12 + 6 = 18 quarts.
• C: This uses 8 per gallon, which is the number of pints in a gallon, not quarts.
• D: This converts the 3 gallons but forgets to add the other 6 quarts.

Answer: A

Correct answer: 3 hours. In 3 hours Pump A fills

of the tank, so 3/4 remains.

Together:

of the tank per hour.

Time left:

• A (correct): Pump A fills 1/4 in 3 hours, leaving 3/4; together the pumps fill 1/4 per hour, so 3 more hours are needed.
• B: This is the total filling time including Pump A's first 3 hours, not the time after Pump B starts.
• C: This is how long both pumps together would take to fill the whole tank, ignoring the part already filled.
• D: This is how long Pump B alone would take to fill the remaining 3/4, leaving out Pump A's help.

Answer: B

Correct answer: $295.20. Total hours:

Pay:

Estimate check: 18 × $16 is about $290.

• A: This is the pay for a single 6-hour shift, not all three shifts.
• B (correct): The worker puts in 3 × 6 = 18 hours, and 18 × $16.40 = $295.20.
• C: This misplaces the decimal point; 18 hours at about $16 is roughly $300, not about $3,000.
• D: This multiplies $16.40 by 3 only, treating each shift as one hour.

Answer: C

Correct answer: 3 hours 30 minutes. Time = distance ÷ speed =

Convert the decimal part:

so the trip takes 3 hours 30 minutes.

• A: This reads the decimal 0.5 as 50 minutes instead of half an hour.
• B: This treats 0.5 hour as 5 minutes; half an hour is 30 minutes.
• C (correct): Time is 210 ÷ 60 = 3.5 hours, and 0.5 hour is 30 minutes.
• D: This adds an extra hour; 60 mph for 4.5 hours would cover 270 miles, not 210.

Answer: B

Correct answer: 456. Total made:

loaves.

Rejected: 5% of

Good loaves:

• A: This is the number of rejected loaves, an intermediate value.
• B (correct): The line makes 80 × 6 = 480 loaves; 5% of 480 is 24, and 480 − 24 = 456.
• C: This is the total made before any loaves are rejected.
• D: This adds the 24 rejected loaves instead of subtracting them.

Answer: C

Correct answer: $90. After 30% off, the customer pays 70% of the original: original × 0.70 = $63.

Divide:

Check: 30% of $90 is $27, and

• A: This adds 30% of $63, but the discount was 30% of the original price, not of the sale price.
• B: This takes another 30% off $63, moving further away from the original instead of undoing the discount.
• C (correct): The sale price is 70% of the original, so the original is $63 ÷ 0.70 = $90.
• D: This adds 30 dollars, treating the percent as a dollar amount.

Answer: A

Correct answer: 630. Car owners:

Two or more cars: 30% of 900 = 270. Exactly one car:

households.

The 30% applies to car owners only, not to every household surveyed.

• A (correct): Car owners are 5/8 × 1,440 = 900; 30% of 900 is 270 with two or more cars, so 900 − 270 = 630 own exactly one.
• B: This is the number of households with two or more cars, not exactly one.
• C: This takes 70% of all 1,440 households, but the 30% applies only to the 900 car owners.
• D: This finds 30% of all 1,440 households, applying the percent to the wrong group and answering the wrong target.

Answer: D

Correct answer: 180. Parts:

so one part is

books. Nonfiction:

Checked out:

On the shelves:

• A: This is the number of nonfiction books checked out, not the number still on the shelves.
• B: This is the total number of nonfiction books before any are checked out.
• C: This works with the fiction count of 400 instead of the nonfiction count.
• D (correct): There are 8 parts of 80 books; nonfiction is 3 × 80 = 240, one-fourth (60) are out, so 180 remain.

Answer: B

Correct answer: 1:15 p.m. Leg 1:

Leg 2:

= 1 hour 30 minutes.

Total: 2 h + 1 h 30 min + 25 min = 3 hours 55 minutes. From 9:20 a.m., that is 1:15 p.m.

• A: This counts only the driving time and leaves out the 25-minute lunch stop.
• B (correct): Driving takes 2 + 1.5 = 3.5 hours, plus 25 minutes, for 3 hours 55 minutes after 9:20 a.m.
• C: This reads 1.5 hours as 1 hour 50 minutes instead of 1 hour 30 minutes.
• D: This converts the 25-minute stop to 0.25 hour, which is only 15 minutes.

Answer: A

Correct answer: $362.52. Subtotal:

After discount:

With tax:

• A (correct): Subtotal $380, discounted to $342, then $342 × 1.06 = $362.52.
• B: This is the price after the discount, before the sales tax is added.
• C: This nets the percents to a 4% discount; the tax is figured on the discounted amount, so the steps cannot simply be combined that way.
• D: This adds the tax to the full $380 and skips the 10% discount.

Answer: D

Correct answer: $720. Add the parts:

One part is

Larger share:

Check:

• A: This is the smaller share (2 parts), not the larger one.
• B: This divides by 3 instead of by the 5 total parts.
• C: This takes 2/3 of the total, treating the ratio 2:3 as a fraction of the whole.
• D (correct): There are 5 parts of $240 each, and the larger share is 3 × $240 = $720.

Answer: A

Correct answer: 12 mph. Times:

rest 0.5 hour,

for 5 hours in all.

Distance:

Average speed:

• A (correct): Total time is 3 + 0.5 + 1.5 = 5 hours for 60 miles, and 60 ÷ 5 = 12 mph.
• B: This averages the two speeds; the average must use total distance over total time.
• C: This divides 60 miles by 4.5 hours of riding and leaves out the 30-minute rest.
• D: This divides the total distance by the first leg's 3 hours only.

Answer: D

Correct answer: $80.00. Run the steps forward: cost × 1.20 = marked price, and marked price × 0.90 = $86.40.

So cost × 1.08 = $86.40, and cost =

Check:

and 90% of $96 is $86.40.

• A: This undoes only the 20% markup and forgets to undo the 10% discount.
• B: This undoes only the 10% discount, giving the marked price instead of the store's cost.
• C: This treats the two changes as a net 10% to remove by subtracting; percent changes are undone by dividing by each multiplier.
• D (correct): Cost × 1.20 × 0.90 = cost × 1.08 = $86.40, so the cost is $86.40 ÷ 1.08 = $80.00.

Answer: A

Correct answer: $840. Only the crew size, hourly rate and hours matter; the stories and the year built are extra facts.

One worker:

Crew:

• A (correct): Each electrician earns 7.5 × $28 = $210, and 4 × $210 = $840.
• B: This is one electrician's pay, not the pay for the whole crew.
• C: This doubles the cost because the house has two stories, but the number of stories does not affect the pay.
• D: This rounds 7.5 hours up to 8 hours for each worker.

Answer: C

Correct answer: 18 gallons. Fuel used:

Fuel left:

You can also find it directly:

• A: This is the amount used, not the amount left.
• B: This is only 1/5 of the tank; 2/5 of the tank is left.
• C (correct): The generator used 3/5 × 45 = 27 gallons, so 45 − 27 = 18 gallons remain.
• D: This subtracts 20 gallons instead of finding 3/5 of 45.

Answer: B

Correct answer: 4 hours. Together they paint

of the fence per hour. In 2 hours:

Remaining:

Painter A alone:

• A: This is how long Painter B alone would need for the remaining 4/9, but Painter B has left.
• B (correct): Together they finish 2 × 5/18 = 5/9, leaving 4/9; at 1/9 per hour, Painter A needs 4 more hours.
• C: This is the total time for the job (2 hours together plus 4 alone), not the extra time.
• D: This subtracts the 2 hours from Painter A's 9-hour time, ignoring the work Painter B did.

Answer: B

Correct answer: $288. Unit rate:

per gallon.

Gallons needed:

Cost:

• A: This is the cost of the 5 gallons in the coverage example, not the paint needed for 2,800 square feet.
• B (correct): Each gallon covers 350 square feet, so 2,800 ÷ 350 = 8 gallons, and 8 × $36 = $288.
• C: This adds the 5 gallons from the example to the 8 gallons needed, buying 13 gallons.
• D: This is the coverage per gallon in square feet, not a cost in dollars.

Answer: D

Correct answer: $178.65. Estimate first:

so the answer must be a little under $180.

Exact:

• A: This is about one-tenth of the right total; an estimate of 9 × $20 = $180 rules it out.
• B: This misplaces the decimal point, giving ten times the true total.
• C: This is the cost of 10 pairs, one more than was ordered.
• D (correct): Nine pairs cost 9 × $19.85 = $178.65, which matches the estimate of about $180.

Answer: C

Correct answer: 66. Bruised: 4% of

Good apples:

Crates:

with 24 apples left over. Only full crates count, so 66 crates are shipped.

• A: This rounds 66.67 up, but the last crate would hold only 24 apples and is not full.
• B: This packs all 2,500 apples and forgets to remove the bruised ones first.
• C (correct): After discarding 100 bruised apples, 2,400 remain; 2,400 ÷ 36 = 66 full crates with 24 apples left over.
• D: This treats 4% as 0.4 and discards 1,000 apples instead of 100.

Answer: C

Correct answer: 10 liters. Parts:

so one part is

Antifreeze: 15 liters; water: 25 liters.

Only antifreeze is added, so the water stays at 25 liters. For a 1:1 ratio, antifreeze must also be 25 liters:

• A: This adds half the difference; the antifreeze must increase by the full 10-liter difference to match the water.
• B: This is the amount of antifreeze already in the mix, not the amount to add.
• C (correct): The mix has 15 liters of antifreeze and 25 of water; adding 10 liters makes 25 liters of each.
• D: This is the amount of water, which stays the same; it is not the amount to add.

Answer: D

Correct answer: $54. Tip: 20% of

Total:

(or

).

• A: This is the tip alone, not the total paid.
• B: This adds 20 dollars instead of 20% of the bill.
• C: This subtracts the tip from the bill instead of adding it.
• D (correct): The tip is 0.20 × $45 = $9, and $45 + $9 = $54.

Answer: C

Correct answer: $2,724. Simple interest: I = principal × rate × time =

Total paid back:

• A: This is the interest alone; the question asks for the loan plus interest.
• B: This includes only one year of interest ($108) instead of three.
• C (correct): Interest is $2,400 × 0.045 × 3 = $324, and $2,400 + $324 = $2,724.
• D: This uses 4.5 as 0.045 per year but multiplies by 4 years instead of 3.

Answer: D

Correct answer: $1,010. Sales that earn commission:

Commission:

Pay:

• A: This pays the 6% commission on all $18,500 instead of only the amount above $10,000.
• B: This is the commission alone; the $500 base pay must be added.
• C: This takes 6% of the $10,000 threshold instead of the sales above it.
• D (correct): Sales above $10,000 are $8,500; 6% of that is $510, and $500 + $510 = $1,010.

Answer: B

Correct answer: 12:15 p.m. Moving apart, the distances add, so the gap grows at

Time:

= 3 hours 15 minutes. From 9:00 a.m., that is 12:15 p.m.

• A: This reads 3.25 hours as 3 hours 25 minutes; 0.25 hour is 15 minutes.
• B (correct): The gap grows at 55 + 65 = 120 mph, so 390 ÷ 120 = 3.25 hours, or 3 hours 15 minutes after 9:00 a.m.
• C: This uses only the faster truck's 65 mph, as if one truck covered the whole 390 miles.
• D: This divides by the average of the two speeds (60 mph) instead of their sum.

Answer: D

Correct answer: $1,120. Work backward. After groceries, 2/3 of the post-rent money is left:

after rent.

After rent, 3/4 of the paycheck is left:

Check: 1/4 of $1,120 is $280, leaving $840; 1/3 of $840 is $280, leaving $560.

• A: This subtracts 1/4 and 1/3 from the whole paycheck, but the 1/3 applies only to what was left after rent.
• B: This undoes only the grocery step and gives the amount left after rent.
• C: This undoes only the rent step and skips the grocery step.
• D (correct): After rent 3/4 is left, and after groceries 2/3 of that, so 1/2 of the paycheck is $560 and the paycheck is $1,120.

Answer: D

Correct answer: 15 miles. Convert the time to hours: 25 minutes = 25/60 hour = 5/12 hour.

Distance = rate × time =

• A: This multiplies 36 by 25 without converting minutes to hours.
• B: This divides 36 by 25 instead of multiplying the speed by the time in hours.
• C: This treats 25 minutes as 0.25 hour, which is only 15 minutes.
• D (correct): Twenty-five minutes is 25/60 of an hour, and 36 × 25/60 = 15 miles.

Answer: A

Correct answer: 325 gallons. Water used: 35% of

Water left:

(or 65% of 500 = 325).

• A (correct): The crew used 0.35 × 500 = 175 gallons, so 500 − 175 = 325 gallons are left.
• B: This is the amount used, not the amount left.
• C: This subtracts 35 gallons instead of 35% of 500.
• D: This adds 35% to the tank instead of taking it away, giving more water than the tank holds.

Answer: B

Correct answer: $0.05. Unit prices:

per battery, and

per battery.

Difference:

per battery.

• A: This is the difference between the two pack prices, not the difference per battery.
• B (correct): The 12-pack costs $0.75 per battery and the 20-pack costs $0.70, a difference of $0.05.
• C: This is the price per battery of the 20-pack, an intermediate value.
• D: This is the price per battery of the 12-pack, an intermediate value.

Answer: A

Correct answer: 8 hours 30 minutes. Split at midnight. From 10:45 p.m. to 12:00 midnight is 1 hour 15 minutes.

From midnight to 7:15 a.m. is 7 hours 15 minutes. Total: 8 hours 30 minutes.

• A (correct): From 10:45 p.m. to midnight is 1 hour 15 minutes, and midnight to 7:15 a.m. is 7 hours 15 minutes, for 8 hours 30 minutes.
• B: This subtracts 7:15 from 10:45 as if both times were on the same half of the day.
• C: This counts one hour too many when crossing midnight.
• D: This counts one hour too few, as if the stretch from 10:45 p.m. to midnight were only 15 minutes.

Answer: A

Correct answer: $198. After the raise:

After the cut:

The second 10% is figured on $220, so it removes $22, more than the $20 added.

• A (correct): The raise gives $220, and 10% of $220 is $22, so the price falls to $198.
• B: This assumes the two 10% changes cancel, but the cut is taken from the larger $220 price.
• C: This is the price after the raise only, an intermediate value before the cut.
• D: This applies only the 10% cut to the original $200 and skips the raise.

Answer: C

Correct answer: 7.5 cups. Flour per serving:

cup.

For 20 servings:

Check: 20 servings is a bit over 3 times 6, so a bit over 6.75 cups makes sense.

• A: This triples the recipe to 18 servings instead of scaling to 20.
• B: This is the flour for one serving, an intermediate value.
• C (correct): Each serving uses 2.25 ÷ 6 = 0.375 cup, and 20 × 0.375 = 7.5 cups.
• D: This adds the 14 extra servings to the cups of flour, mixing servings with cups.

Answer: D

Correct answer: $254.88. Daily charge:

Extra miles:

so mileage is

Before tax:

With 8% tax:

• A: This is the charge before the 8% tax is added.
• B: This charges $0.25 for all 470 miles instead of only the 320 miles over 150.
• C: This taxes only the daily charge and leaves out the mileage charge.
• D (correct): Daily charge $156 plus mileage 320 × $0.25 = $80 gives $236, and $236 × 1.08 = $254.88.

Answer: A

Correct answer: 24 minutes. Add the rates:

of the batch per minute.

Time:

which is faster than either copier alone, as it should be.

• A (correct): Together they print 1/40 + 1/60 = 1/24 of the batch per minute, so the job takes 24 minutes.
• B: This averages the two times; working together must be faster than either copier alone.
• C: This adds the two times, which would be slower than either copier alone.
• D: This halves the faster copier's time, as if both copiers were as fast as Copier A.