ACT Math Prep: Story Problems About Money
The ACT math section explores several different mathematic concepts that students are expected to have a solid understanding of in order to succeed at the college level. One of these concepts is real-life mathematical problems related to money. Here, we’re walking through some easy and some hard math story problems related to money that students could see on the ACT.
Money is important. There’s no doubt about that. Money is an important tool that runs our society and our lives in many ways, and, you know what? Money is math.
There are many concepts tested throughout the ACT math section that students may wonder about the usefulness of in real life. For example, where will a student use polynomials and complex algebra in everyday life? I don’t know even know the answer to this. Basic algebra and geometry can for sure come in handy, but it could be argued that there is nothing more useful that students should have an understanding of than mathematics as they relate to money.
And yet, money is a topic that many high schoolers aren’t taught a whole lot about during high school. Sure, students will understand how to count change and add and subtract money amounts, but most will have a small understanding of things like interest and investing — important knowledge that will help them in their adult lives.
ACT math questions about money inquire about sales, interest accrual, percentage value, and more. Here, we’re taking a look at some examples of money math problems as they’ve shown up on the ACT in the past.
Easy ACT Money Math Problems
Averages -
Students can pretty much assume they they will be thrown an average — or “mean” — question early on during the ACT math section. This could show up in many forms requiring students to find the mean, such as in a list of random numbers, the ages of a group of people, money amounts, or more.
All in all, finding the mean of any group of values is calculated the same way:
ADD ALL VALUES TOGETHER & THEN DIVIDE BY THE TOTAL NUMBER OF VALUES
Looking at question #1 below, this meant to be an incredibly easy question, as it shows up as #1 in this section. (The ACT Math section is ordered from easy question to hard questions.)
To solve #1 above, there are a few steps to go through. First, you need to calculate the total that Xuan made on the 9 books she sold. You do this by multiplying 9 x $9.80 — this gives you a total of $88.20.
Next, you know that she turns around and buys 4 new books. That amount comes out of the $88.20 that she just made by selling books, but you don’t know what she spent on the new books — that is what you’re trying to find. You do know what she has left over, so you have to subtract it. $88.20 - $37.80 = $50.40 — this is the amount of money that Xuan spent on 4 new books.
Now, you know that 4 books totaled $50.40, so, to find the average, you simply divide by 4.
$50.40 / 4 = $12.60
The correct answer is D.
Straightforward Multi-Step Money Problems -
Many money problems that you may be confronted with on the ACT will include simple operations like addition, subtraction, and multiplication.
Question #4 below is a good example of a straightforward money-related problem that you could see early on during the ACT math section. All this question requires to get to the answer is basic subtraction, addition, and division.
We know that Juan pays $10 for 300 text messages and then an additional $0.10 per text message after the initial 300. We also know that Juan spent $16.50 on his last phone bill.
To calculate, we would first subtract the $10, knowing that that paid for the first 300 texts. That leaves Juan with $6.50 in additional text messages.
Now, we need to divide that $6.50 by $0.10 to determine how many additional texts Juan sent.
$6.50/$0.10 = 65 — this is the number of additional texts that Juan sent.
Then you have to add back in his original 300 that went with the first $10.
300 + 65 = 365
The correct answer is J
Down Payment & Car Payments -
Now and then, the ACT will include money questions about down payments on cars and houses. When you make an expensive purchase that you want to pay for over a period of time, you’ll often have to pay a down payment. This is money paid upfront. Question number #10 below is an example of calculating the amount of money spent paying for something over time compared to paying the full amount at once.
In #10 above, we are told that Diego is buying a car that is priced at $13,400. We know that he pays $400 as a down payment and has received a loan for the rest of the car, which he will pay over the course of 48 payments. Each payment is $300.
Here is what we can figure out: We know that there will be 48 payments of $300. We can calculate how much will be spent over these 48 months by using simple multiplication.
48 x $300 = $14,400 — this is the amount Diego spends on the car payments.
We also know that Diego paid $400 as a down payment. We have to add this to the amount he spends on payments.
$14,400 + $400 = $14,800 — this is the total that Diego spent on the car.
We know that the car was originally priced at $13,400. Now we use subtraction to find the difference between what Diego paid and what the cost was of the car.
$14,800 - $13,400 = $1,400
The correct answer is G
Note: The reason that Diego pays more for the car by paying over a long time period than he would if he just paid for the car at once is because of INTEREST. Interest is a percentage fee that is paid to the lender in exchange for them loaning money in the first place.
Consumer Purchases -
Oftentimes, ACT math problems related to money will revolve around people purchasing items — TVs, shoes, clothing, etc.
Question #11 below is a good example of a consumer purchases question you could see on the ACT.
We know that Ben wants to buy a $495 TV, so he opens a savings account and deposits $75 initially. He then deposits an additional $65 each month.
We need to find how long it will take for Ben to end up with $495 in his savings account that he can spend on the TV he wants. To do this, we first have to subtract his initial deposit of $75 from the cost of the TV, as he already has those funds.
$495 - $75 deposit = $420 to go before he can buy the TV.
Deposits into savings account:
Month 1: $75 already there + $65 deposit = $140
Month 2: $140 already there + $65 deposit = $205
Month 3: $205 already there + $65 deposit = $270
Month 4: $270 already there + $65 deposit = $335
Month 5: $335 already there + $65 deposit = $400
Month 6: $400 already there + $65 deposit = $465
Month 7: $465 already there + $65 deposit = $530 — now he has the $495 he can spend on a TV.
The answer is C.
Note - A faster route to this question would be to calculate the following:
$420 / $65 = 6.4 months until he has $475 in his savings account. You have to round this up to 7 months.
Hourly Wages -
You can also anticipate seeing money questions that discuss how much money someone is paid hourly. Here, we find out that Jorge is going to get a 6% increase to his hourly rate of $12.00.
To work through this question, you need to be familiar with basic percentages. We know that Jorge makes $12.00 an hour, and we need to figure out what 6% of that is.
$12.00 x 0.06 = $0.72
We multiplied by 0.06 because that is the decimal form of 6%.
Now we know that the $0.72 is 6% of $12.00, so, since Jorge is getting an pay INCREASE, we have to ADD that total to his hourly rate.
$12.00 + $0.72 = $12.72
The correct answer is H.
Percentages -
Similar to the question we just worked through about Jorge’s hourly rate, the question below also involves calculating basic percentages.
Bella sells a house for $250,000 and she gets to keep 3% of the sale price.
Again, we have to start by finding what 3% of $250,000 is.
$250,000 x 0.03 = $7,500 - this is the amount that Bella gets to keep
0.03 is the decimal form of 3%
The correct answer is D.
Hard ACT Money Math Problems
Property assessment -
Question #9 below is actually meant to be an easier math problem, as it shows up early as question #9. While the math involved is pretty simple, we’ve found that many students actually struggle with this question simply because they aren’t familiar with the concepts discussed in the question.
Question #9 above asks about how property is assessed. This is definitely not a topic that many high schoolers will be familiar with. All this means is that we want to work with only 3/4 of the $56,000 mentioned in this question.
We need to start by calculating what 3/4 (or 75%) of $56,000 is.
$56,000 x 0.75 = $42,000 - this is the house value that we will be working with to determine what is paid in taxes.
Now, we know that tax is calculated at a rate of $3 for every $100 of assessed value.
Assessed value is $42,000, so now we have to figure out how many times $42,000 can be divided by $100.
$42,000 / $100 = 420
Now we multiply 420 by $3 each.
420 x $3 = $1260 - this is the total that will be paid in taxes.
The correct answer is C.
Forming Equations -
One way that the ACT can make money math questions more difficult is by removing many of the numbers and replacing them with variables.
Variables can be a lot trickier than numbers simply because you have to think about how different aspects of an equation are related. This leaves a bit more room for error compared to working with real numbers and testing actual equations, where you’ll end up with a clear right or wrong answer.
For question #37 above, you are tested with determining the appropriate equation for the profit on the batches of cookies that Suzanne and Chad are making.
Since you are given a lot of information in the story about what the cookies cost and other expenses, this is a great problem where you should TEST REAL NUMBER EXAMPLES.
Choose a random value for b and test it.
Lets pretend that Suzanne and Chad make 8 batches of cookies — b = 8
Before looking to the answer options, I can work through what it will cost and how much money they will make on 8 batches of cookies just by using the information I’m given in the question.
I know it costs $4 per batch for the ingredients. 8 batches x $4 = $32 expenses. They also buy a mixer one time for $50. That brings the total expenses to $32 + $50 = $82.
I also know that they are going to sell the cookies for $5 per batch. $8 x $5 = $40 that they will make on this batch of cookies. Their total profit will end up negative, as they’ve spent more than they’ve made.
Total profit = $40 - $82 = -$42 = P
Now, it’s okay that this ends up negative. I’m just testing a random value. What I have to do now is look to the answer options and then RETEST this same value of b = 8.
If you can rule out any of the answer options, that’s great. That will speed you along. If not, you can simply test b = 8 for all 5 answer options, and only one answer option should give you the result of P = -$42.
The correct answer is E.
*NOTE: When you replace variables with numbers and test them, you can use any integer you would like, but it is recommended that you avoid using values 1 and 0, as they have particular rules when it comes to operations such as multiplication and division.
Equation Sets -
Question #22 below is similar to question #37 that we just completed above. Here, however, you are given two equations to figure out instead of just one. When you’re working with two related equations, this is called a SYSTEM OF EQUATIONS.
For this set of equations, you should actually be able to work through the story problem and assess the relationships between the different parts. That means there should not be a need to replace the variables with actual number values, but you can always do this if you get stuck.
Consider the relationships that we’re told about. We know that an appetizer costs twice as much as a slice of pizza. That means I can determine that this equation would work for part of this set:
Appetizer = Pizza x 2 — this becomes…
a = 2p
We also know that Odetta spends $8.75 on 2 appetizers and 3 slices of pizza.
That means we know that:
$8.75 = 2a + 3p
If you look at the answer options above, F is the only answer that contains BOTH of these two equations.
There is no need to go any further with this question.
The correct answer is F.
Money & Algebra -
Question #24 below requires students to incorporate some algebra into their money calculations. Upon first reading this question, it can be confusing where to start. In fact, you have to flip-flop what you’re given to work through this question.
We are told that “if [John] spent up to $30 from his savings account, his savings account would have at least 3/4 as much in it as it has now.” The question can be rephrased as $30 is at least 25% of what is in John’s savings account. What is in John’s savings account?
This equation would be set up as follows: $30 = 0.25x
Now, all you have to do is use basic algebra and divide 30 by .25, which will give you $120.
The correct answer is K.
While we may not have been able to cover every single type of money math problem that you could see on ACT day, these are some big concepts that have shown up on multiple ACT exams. That being said, make sure you understand how to work with percentages, interest, fees, tax, and basic addition, subtraction, multiplication, and division as they pertain to money.
Hopefully you found this post helpful and will find yourself adequately prepared for tackling all money problems you run into on the ACT!
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