### All SAT Math Resources

## Example Questions

### Example Question #58 : 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?

**Possible Answers:**

**Correct answer:**

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 #152 : Algebra

George is three times older than Joey. The sum of their ages is 16. What is the product of their ages?

**Possible Answers:**

**Correct answer:**

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 #153 : Algebra

Three consecutive even numbers add to 42. What is the middle number?

**Possible Answers:**

**Correct answer:**

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 #151 : Algebra

Consider the following equation:

Which of the following must be true?

**Possible Answers:**

**Correct answer:**

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 #152 : Algebra

If

,

then

**Possible Answers:**

**Correct answer:**

Divide both sides by 300 to get . Subtract 7 and divide by two 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?

**Possible Answers:**

56

108

104

38

**Correct answer:**

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 #1 : How To Find The Solution To An Equation

If x = 4, and y = 3x + 5, then 2y – 1 equals

**Possible Answers:**

47

22

15

33

**Correct answer:**

33

Start by plugging in x = 4 to solve for y: y = 3 * 4 + 5 = 17. Then 2 * 17 – 1 = 33

### Example Question #61 : 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?

**Possible Answers:**

34

24

32

36

**Correct answer:**

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 #1 : 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?

**Possible Answers:**

2

5

8

7

**Correct answer:**

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?

**Possible Answers:**

22

27

17

13

**Correct answer:**

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.

Certified Tutor

Certified Tutor