All SAT Math Resources
Example Questions
Example Question #51 : Algebra
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 = the number of birdhouses sold each month.
Substituting in 50 for gives an answer of 500, so the profit on 50 birdhouses is $500.
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 = Joey's age and = George's age.
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 = 1st even number, = 2nd even number, and = 3rd even number.
Then the equation to solve becomes .
Thus , so the middle number is 14.
Example Question #54 : Algebra
Consider the following equation:
Which of the following must be true?
The quantity inside the absolute value brackets must equal either or , depending on whether the quantity inside the brackets is positive or negative. We therefore have two seperate equations:
To solve the first equation, add 9 to both sides:
Subtract from both sides:
This is the first solution. Now let's look at the second equation. The distributive law gives us:
Add 9 to both sides:
Add to both sides:
Divide both sides by 3:
Therefore, is either 4 or 6.
Statement does NOT have to be true because can also equal 4.
Statement must be true because both 4 and 6 are positive .
Finally, statement always holds because 4 and 6 are both even.
Example Question #52 : Algebra
If
,
then
Divide both sides by 300 to get . Subtract 7 and divide by two to get .
Example Question #51 : Linear / Rational / Variable Equations
What is the value of (5 + x)(10 – y) when x = 3 and y = –3?
108
56
38
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 #1831 : Sat Mathematics
If x = 4, and y = 3x + 5, then 2y – 1 equals
33
15
22
47
33
Start by plugging in x = 4 to solve for y: y = 3 * 4 + 5 = 17. Then 2 * 17 – 1 = 33
Example Question #1832 : Sat Mathematics
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
36
34
32
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 #54 : Linear / Rational / Variable Equations
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?
7
2
8
5
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 #1 : 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?
22
27
13
17
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.