Money, Interest and Everyday Quantities

0:00 Hey there, so if you're getting ready for the ASVAB and the arithmetic reasoning section has you feeling, you know, a little stressed, take a deep breath, you're in exactly the right place. Today, we're going to build your confidence in solving everyday money problems entirely by hand. That means no calculators, no panic, just a clear logical toolkit you can rely on when test day actually arrives. By the time we wrap up this explainer, you're going to see that this math is absolutely manageable. Okay, let's dive right into this. We're looking at a pretty straightforward agenda today to build up your skills step by step. We'll start off with money basics, then scale up to wages and interest, unlock some really helpful mental math shortcuts with real worked examples, and finally we'll finish with a check yourself section to test your new skills. Alright, section one, money basics. The foundation of everything we're about to do here is beautifully simple. All money math starts with treating dollars and cents as simple decimals. When you're calculating by hand, the absolute golden rule is to line up your decimal points. It's kind of like stacking blocks.

1:03 If you buy items for $12.75, $8.40, and $3.09, you just line those decimals right up vertically, add them together, and boom, you get $24.24. Now, if you hand the cashier a $30 bill, you set up $30 minus $24.24. Again, keep those decimals perfectly aligned. That gives you $5.76 in change. Now, what about finding the absolute best deal at the store? That's where unit price comes in, which is literally just the total cost divided by the number of units. So if a six-pack of soda is $5.34, you take $5.34 divided by 6, and that equals a unit price of 89 cents per can. Now, let's talk about percentages when you're shopping. A discount is simply a percentage taken off the original price. For 30% off a $64 item, you take 0.30 times $64, which is $19.20. Subtract that from $64, and your sale price is $44.80. Sales tax, on the other hand, works the exact opposite way. It's added on. For a 6% tax on an $85 purchase, you find 6% of $85, which is $5.10, add that tax to the $85, and your final total comes to $90.10.

2:13 Wages and interest. We're shifting from the store to the workplace, and larger financial concepts here. But I want to reassure you right now, the exact same math rules apply. We're just using them for paychecks and loans. Let's see how this builds into calculating your hourly wages. Gross pay is literally just your hourly rate times the hours you work. So at 21.40 an hour for 35 hours, that's 21.40 times 35, giving you $749. But what about overtime? Overtime is usually paid at time and a half, meaning 1.5 times the regular rate. But here's the kicker. It only applies to hours over 40 in a single week. So say you make 24 an hour and work 48 hours. You've got to split it up. Regular pay is 40 times 24, which equals 960. Your overtime pay is those 8 extra hours multiplied by your new $36 overtime rate, which equals 288. Add those together, and your total is 1,248. This exact same percentage logic applies everywhere else too. Commission is just a percent of sales.

3:15 A 7% commission on 18,500 is 0.07 times 18,500, which gives you $1295. A retail markup? That's just an amount added to a seller's cost to set a price. A 40% markup on a $45 item is 0.40 times 45, which equals 18. Add that 18 to the 45 and the new price is $63. And restaurant tips? Just break them down in your head. An 18% tip on $55? Think about it. 10% is 5.50. 5% is 2.75, and 3% is 1.65. Add them up. 5.50 plus 2.75 plus 1.65 equals exactly $9.90. When you see budget questions, please don't let a wall of numbers intimidate you. A budget is really just careful addition, followed by one big subtraction to find what's left. Imagine an income of $2,400. We simply add up the expenses first. 950 for rent, 420 for food, 185 for transport, and 160 for utilities. That totals $1,715.

4:19 Subtract that total from the $2,400 income, and you have a remaining balance of exactly $685. Now what's really interesting here is the simple interest formula. i equals p times r times t. If you deposit $3,000 at 4% for 5 years, it's 3,000 times .04 times 5, which equals $600 in interest. Listen, the absolute most crucial thing to remember here is that t must always be in years. Always. If a test gives you 18 months, you have to divide by 12 to make it 1.5 years. You can also reverse this whole thing. If you know a $2,500 deposit earns $250 over two years, you divide the interest by the principal times the time. So $250 divided by the result of $2,500 times 2 equals .05, or a 5% rate. Let's wrap up this section with profit and multi-step math. Profit is literally just revenue minus cost. Spend $240 on shirts and sell them for $360. Profit is $360 minus $240, which is $120. Now, for multi-step transactions, you absolutely must do the math in the exact order the events happen.

5:28 If you buy $78 worth of clothes with a 10% coupon, apply that discount first to get $70.20. Then the 5% tax is applied to that new amount. $70.20 times 1.05 equals a final price of $73.71. Just remember this rule. Tax always, always applies after the discount. Alright, section three, shortcuts and examples. It's time to unlock those mental math cheat codes and prove that this toolkit works with actual test-style examples. When you don't have a calculator, these shortcuts are going to save you so much time. To find 10% of anything, just slide the decimal point one place to the left. Need 5%, take that 10%, and just cut it in half. For 25%, simply divide the number by 4. For 50%, divide by 2. But, guys, the real game changer for passing is understanding shifting bases. A 20% drop, followed by a 20% increase, does not return you to where you started. Think about it. If 100 drops 20%, it becomes 80. Increasing that new 80 base by 20%, only brings you up to 96.

6:33 So, always, always ask yourself, which amount does this percent apply to right now? Let's put this into practice. Worked example one, unit price. Say, a 5-pound bag is $7.45, and an 8-pound bag is $11.60. $7.45 divided by 5 equals $1.49 per pound. $11.60 divided by 8 equals $1.45 per pound. By breaking it down, it's super clear the 8-pound bag is the better deal. And this brilliantly illustrates our rule about the shifting base. Worked example two, a $90 jacket is 30% off with 5% tax. If it's 30% off, you're paying 70%, right? 0.70 times 90 equals a $63 sale price. That 5% tax applies to the 63, not the original 90. So, 63 times 1.05 equals a final price of $66.15. Next up, worked example three, overtime. A tech earns $22 an hour, gets time and a half after 40 hours, and works a 46 hour week. Let's slowly trace this math.

7:36 The first 40 hours are regular pay. 40 times 22 equals 880. The overtime rate is 1.5 times 22, which is 33. We have six extra hours, so 6 times 33 equals 198. Add them together. 880 plus 198 equals a total gross pay of $1,078. Worked example four is a straight plug-and-play for simple interest. $4,000 at 3% for two years. We just multiply the principal, the rate as a decimal, and the years. Interest equals 4,000 times 0.03 times two, which gives us a final interest of $240. For worked example five, a household earns 3,200 a month. They spend 960 on rent, 480 on savings, and 1,150 on bills. To find what's left, we subtract those directly from the income. 3,200 minus 960 minus 480 minus 1,150 equals 610 dollars remaining. Finishing up our examples with worked example six, an agent earns a $600 base plus a 3% commission on $20,000 of sales.

8:46 First, let's find the commission. 0.03 times 20,000 equals 600. Then add that calculated commission back to the base pay. 600 plus 600 equals a total check of $1,200. Okay, real quick, before we practice, I want to spotlight some common traps so you know exactly what to avoid on test day. 1, stopping early. This means finding a discount amount but forgetting to actually subtract it from the total. Always reread the question. Next, do not add percent across steps. 25% off then 8% tax is not a flat 17% off. Another huge one. Paying all hours at the overtime rate instead of just the hours over 40. Watch out for using months instead of years. Always convert to years. And finally, using the wrong base. Remember, a second discount applies to the newly reduced price, not the original tag. All right, section 4, check yourself. It's time to put your brand new calculator free toolkit to the test with two real practice questions. Let's see what you've got.

9:51 Here's question 1. A package of 8 AA batteries costs $9.92. What is the price per battery? A, $79.36. B, 81 cents. C, $1.24. Or D, $1.92. Take a quick second to mentally calculate that unit price. Got it? And the answer is C, $1.24. If you got that, nicely done. As we covered, finding a unit price is simply dividing the total cost by the number of units. So $9.92 divided by 8 equals exactly $1.24 per battery. Let's look at our final question. Question 2. A family's restaurant bill is $46. They want to leave a 15% tip. How much is the tip? A, $6.90. B, $4.60. C, $2.30. Or D, $52.90. Take a second and remember to use that 10 and 5% mental shortcut we just talked about. Okay. So the crucial point here is breaking this down without a calculator. The answer is A, $6.90.

10:57 You find 10% by shifting the decimal one place left, giving you $4.60. Then 5% is just half of that, which is $2.30. Add $4.60 and $2.30 together, and your total 15% tip is $6.90. See? You now have the toolkit to handle decimals, unit prices, wages, and interest completely by hand. So my question to you is, now that you have these mental math cheat codes, what else can you calculate in your daily life? You might be surprised at how much easier the world looks when you can do the math right in your head. Thanks for joining me on this explainer and happy studying.