SAT Math : Linear / Rational / Variable Equations
Study concepts, example questions & explanations for SAT Math
All SAT Math Resources
Example Questions
Example Question #91 : How To Find The Solution To An Equation
Pets Plus makes bird houses. Their monthly fixed expenses are $750. The cost for each bird house is $15. The bird houses sell for $40.
If Pets Plus sells 50 bird houses, what is the profit?
Let 
Substituting in 50 for 
Example Question #52 : Algebra
George is three times older than Joey. The sum of their ages is 16. What is the product of their ages?
Let 
Then the equation to solve becomes 
Therefore, Joey is 4 years old and George is 12 years old, so the product of their ages is 48.
Example Question #53 : Algebra
Three consecutive even numbers add to 42. What is the middle number?
Let 
Then the equation to solve becomes 
Thus 
Example Question #51 : Equations / Inequalities
Consider the following equation:
Which of the following must be true?
The quantity inside the absolute value brackets must equal either 
To solve the first equation, add 9 to both sides:
Subtract 
This is the first solution. Now let's look at the second equation. The distributive law gives us:
Add 9 to both sides:
Add 
Divide both sides by 3:
Therefore, 
Statement 
Statement 
Finally, statement 
Example Question #51 : Algebra
If
then
Divide both sides by 300 to get 
Example Question #1 : How To Find The Solution To An Equation
What is the value of (5 + x)(10 – y) when x = 3 and y = –3?
56
38
108
104
104
This is a simple plug-in and PEMDAS problem. First, plug in x = 3 and y = –3 into the x and y. You should follow the orders of operation and compute what is within the parentheses first and then find the product. This gives 8 * 13 = 104. The answer is 104.
Example Question #51 : Algebra
If x = 4, and y = 3x + 5, then 2y – 1 equals
47
15
33
22
33
Start by plugging in x = 4 to solve for y: y = 3 * 4 + 5 = 17. Then 2 * 17 – 1 = 33
Example Question #51 : Algebra
Sarah’s current age is three times Ron’s age two years ago. Sarah is currently 14 years older than Ron. What is the sum of Sarah and Ron’s current age?
24
32
36
34
34
The best way to solve this problem is to turn the two statements into equations calling Sarah’s age S and Ron’s age R. So, S = 3(R – 2) and S = 14 + R. Now substitute the value for S in the second equation for the value of S in the first equation to get 14 + R = 3(R – 2) and solve for R. So R equals 10 so S equals 24 and the sum of 10 and 24 is 34.
Example Question #4 : How To Find The Solution To An Equation
A store sells potatoes for $0.24 and tomatoes for $0.76. Fred bought 12 individual vegetables. If he paid $6.52 total, how many potatoes did Fred buy?
5
8
7
2
5
Set up an equation to represent the total cost in cents: 24P + 76T = 652. In order to reduce the number of variables from 2 to 1, let the # tomatoes = 12 – # of potatoes. This makes the equation 24P + 76(12 – P) = 652.
Solving for P will give the answer.
Example Question #2 : How To Find The Solution To An Equation
Kim is twice as old as Claire. Nick is 3 years older than Claire. Kim is 6 years older than Emily. Their ages combined equal 81. How old is Nick?
13
27
17
22
17
The goal in this problem is to have only one variable. Variable “x” can designate Claire’s age.
Then Nick is x + 3, Kim is 2x, and Emily is 2x – 6; therefore x + x + 3 + 2x + 2x – 6 = 81
Solving for x gives Claire’s age, which can be used to find Nick’s age.
All SAT Math Resources
