All ACT Math Resources
Example Questions
Example Question #41 : Expressions
What is the value of that satisfies the equation
?
Distributing the 5 on the left side of the equation gives you .
Subtracting from both sides of the equation gives you
.
Adding 5 to both sides of the equation gives you .
Dividing each side of the equation by 7 gives you .
Example Question #11 : How To Evaluate Algebraic Expressions
If and
, what is
?
Example Question #12 : How To Evaluate Algebraic Expressions
8 less than 4 times a number is 76. Find the number.
Example Question #13 : How To Evaluate Algebraic Expressions
Let ,
and
. Solve
Substitute the given values into the variables to get:
Example Question #13 : How To Evaluate Algebraic Expressions
Bob needs to order candy bars from a warehouse. The website he is ordering from shows that the candy bars come in cases of
boxes with
candy bars in each box. It is not possible to order partial cases. What is the fewest amount of cases that Bob should order?
The answer is .
Bob must order full cases, which contain boxes of candy bars with
bars per box. This comes out to a total of
candy bars per case. An order of
cases comes out to
candy bars which is not enough. However if he orders one more case, the total comes out to
candy bars which allows him to barely surpass his needed amount of
bars.
Example Question #11 : How To Evaluate Algebraic Expressions
Solve for :
The answer is .
To solve this equation for , first distribute the
to make the equation
. Next, subtract
from both sides to leave you with
. Finally, divide both sides by
to determine that
.
Example Question #12 : How To Evaluate Algebraic Expressions
If three chairs cost , what is the cost of
chairs?
The answer is .
If three chairs cost , each chair costs
. To determine the cost of two chairs, multiply
.
Example Question #13 : How To Evaluate Algebraic Expressions
Evaluate the expression for
The answer is
To solve this expression subsitute for
. This results in
. Simplify to get
as the answer.
Example Question #14 : How To Evaluate Algebraic Expressions
If 40% of equals 8, then
The equation can be set up as follows:
Solve for
Now that we know the value of , we can plug it in to our final equation:
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 #15 : How To Evaluate Algebraic Expressions
If , then what is
?
One can arrive to the answer two ways. They can either use FOIL then plug in for
, or they can plug in
for
first, and then solve.
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 for
, we have:
Which simplifies to,
or
Certified Tutor
Certified Tutor
All ACT Math Resources
![Learning Tools by Varsity Tutors](https://vt-vtwa-app-assets.varsitytutors.com/assets/problems/og_image_practice_problems-9cd7cd1b01009043c4576617bc620d0d5f9d58294f59b6d6556fd8365f7440cf.jpg)