ACT Math : Equations / Inequalities
Study concepts, example questions & explanations for ACT Math
All ACT Math Resources
Example Questions
Example Question #7 : How To Find The Solution For A System Of Equations
If Sally makes $9.50 an hour, what was her gross pay for the week if she gets paid time-and-a-half for any hours above 40?
$493.75
$380.00
$564.25
$355.50
$451.25
$451.25
Sally works 40 regular hours and 5 overtime hours. Her regular hourly pay becomes 40 * 9.50 = $380.00, and her overtime pay becomes 5 * 9.50 * 1.5 = $71.25, so her weekly gross (before taxes) pay is $451.25
Example Question #4 : How To Find The Solution For A System Of Equations
Sally sells cars for a living. She has a monthly salary of $1,000 and a commission of $500 for each car sold. How much money would she make if she sold seven cars in a month?
$4,000
$5,000
$5,500
$4,500
$3,500
$4,500
The commission she gets for selling seven cars is $500 * 7 = $3,500 and added to the salary of $1,000 yields $4,500 for the month.
Example Question #5 : Systems Of Equations
John's age is half of Bob's age in 2010. John is also 3 years younger than Bob in 2010.
How old is Bob in 2013?
3
5
9
6
10
9
Using algebra, we can write the system of equations J = (1/2)B and J + 3 = B, where J is John's age in 2010 and B is Bob's age in 2010.
We plug in and get that J = 3 and B = 6
So 3 years later in 2013, we know Bob is 9 years old.
Example Question #6 : How To Find The Solution For A System Of Equations
Given the system of equations:
2x + 3y = 15
x + 3y = 0
What is x?
–15
15
5
–5
0
15
Substitute the second equation into the first to find that y = –5. Then plug y = –5 into either equation to find x = 15.
Example Question #1992 : Act Math
Solve the system of equations:
2x + 3y = 10
x – 2y = –2
no solution
x = 0, y = 1
x = 2, y = 1
x = 0. y = 2
x = 2, y = 2
x = 2, y = 2
Use elimination to solve for one variable.
y = 2
Back substitute for the other variable.
x = 2
Example Question #1993 : Act Math
Given the system of equations:
2x + 2y = 12
x – y = 2
What is x equal to?
1
–2
8
4
2
4
Substitute the second equation into the first or use elimination.
Example Question #1994 : Act Math
Find a solution to the system of equations:
2x – y = 0
x + y = 3
(1,2)
(0,2)
(2,1)
(1,0)
(0,0)
(1,2)
Use substitution and plug in to solve for one equation. Then use back substitution to solve for the other variable.
Example Question #1995 : Act Math
Tom's allowance is 3 times as much as Joe's allowance. If the sum of their allowance is $56, how much is Joe's allowance?
Tom's allowance (
The sum of their allowance is $56.
Restate the second equation by substituting 
Example Question #11 : Systems Of Equations
Solve
What is the sum of 
Add the two equations to get
or
and then substitute 
Solving for 
And we then substitute 
So the sum of 
Example Question #1997 : Act Math
Jacob counts his money as he puts it in his new piggy bank. He has the same number of dimes as quarters and twice as many nickels as dimes. He has $2.25 total. How many dimes does he have?
The general equation to use is:
where 
Let 
So the equation to solve becomes
Solving shows that Jacob had 10 nickels, 5 dimes and 5 quarters for a total of $2.25.
All ACT Math Resources
