ACT Math : Expressions
Study concepts, example questions & explanations for ACT Math
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Example Questions
Example Question #11 : How To Evaluate Algebraic Expressions
Solve for 
The answer is 
To solve this equation for 
Example Question #17 : Evaluating Expressions
If three chairs cost 
The answer is 
If three chairs cost 
Example Question #11 : How To Evaluate Algebraic Expressions
Evaluate the expression 
The answer is
To solve this expression subsitute 
Example Question #19 : Evaluating Expressions
If 40% of 
The equation can be set up as follows:
Solve for
Now that we know the value of 
Remember, in this scenario, we must follow proper order of operations, where power is taken in consideration before multiplication.
In other words, 20 is squared first, giving 400.
In our last step, we multiple 400 by 0.5, giving our final answer: 200
*Note, the other answer choices generally consist of answers at other steps of the problem or answers arrived at when not following proper order of operations. Be careful when answering questions like these, as they often have other answer choices meant to catch your mistake on the ACT.
Example Question #20 : Evaluating Expressions
If 
One can arrive to the answer two ways. They can either use FOIL then plug in 
We recommend using the latter approach, as it saves more time, an important skill to recognize to be successful on the ACT.
By plugging in 
Which simplifies to,
Example Question #21 : How To Evaluate Algebraic Expressions
What is the value of z that satisfies the equation: 10(z – 6) = 8z + 4
32
28
34
5
–32
32
Distribute: 10z – 60 = 8z + 4
Move all like terms together: 2z = 64
Solve: z = 32
Example Question #22 : Evaluating Expressions
If 
Divide both sides by 
Example Question #23 : Evaluating Expressions
Find the value of 
This problem requires utilization of the opposite operations to both sides principle.
Adding +2 to both sides yields
Subtracting 2y from both sides yields
Example Question #51 : Expressions
Sally is ordering snacks for her class trip. She needs 85 cookies. The cookies come in cases of 6 boxes, with 7 cookies in each box. Sally can't order a partial box. What is the smallest number of cases she should order?
1
4
6
2
3
3
We first determine how many cookies are in each box. There are 7 cookies in a box, multiplied by 6 boxes, making 42 cookies in a case. We then divide the total number of cookies she needs, 85, by the number in each case, 42, giving us 2 with a remainder. This means Sally must order 3 cases of cookies.
Example Question #52 : Expressions
A company rents cars for a rental fee of $37.00 per day, with an additional charge of $0.45 per mile driven. Which of the following expressions represents the cost, in dollars, of renting the car for 2 days and driving it m miles?
37m + 45
37m + 0.45
74m + 45
0.45m + 37
0.45m + 74
0.45m + 74
To determine cost we add the initial rental fee of $37, times two days giving us $74 plus the mileage rate, 0.45, times the number of miles. Giving an equation of 0.45m+74.
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