### All New SAT Math - Calculator Resources

## Example Questions

### Example Question #1 : Solving Systems Of Equations In Word Problems

Mark is three times as old as his son Brian. In ten years, Mark will be years old. In how many years will Mark be twice as old as Brian?

**Possible Answers:**

**Correct answer:**

In ten years, Mark will be years old, so Mark is years old now, and Brian is one-third of this, or years old.

Let be the number of years in which Mark will be twice Brian's age. Then Brian will be , and Mark will be . Since Mark will be twice Brian's age, we can set up and solve the equation:

Mark will be twice Brian's age in years.

### Example Question #2 : Solving Systems Of Equations In Word Problems

Gary is twice as old as his niece Candy. How old will Candy will be in five years when Gary is years old?

**Possible Answers:**

Not enough information is given to determine the answer.

**Correct answer:**

Since Gary will be 37 in five years, he is years old now. He is twice as old as Cathy, so she is years old, and in five years, she will be years old.

### Example Question #1 : Solving Linear Equations In Word Problems

Erin is making thirty shirts for her upcoming family reunion. At the reunion she is selling each shirt for $18 apiece. If each shirt cost her $10 apiece to make, how much profit does she make if she only sells 25 shirts at the reunion?

**Possible Answers:**

**Correct answer:**

This problem involves two seperate multiplication problems. Erin will make $450 at the reunion but supplies cost her $300 to make the shirts. So her profit is $150.

### Example Question #1 : Solving Linear Equations In Word Problems

Write as an equation:

"Ten added to the product of a number and three is equal to twice the number."

**Possible Answers:**

**Correct answer:**

Let represent the unknown quantity.

The first expression:

"The product of a number and three" is three times this number, or

"Ten added to the product" is

The second expression:

"Twice the number" is two times the number, or

.

The desired equation is therefore

.

### Example Question #2 : Solving Linear Equations In Word Problems

Write as an equation:

Five-sevenths of the difference of a number and nine is equal to forty.

**Possible Answers:**

**Correct answer:**

"The difference of a number and nine" is the result of a subtraction of the two, so we write this as

"Five-sevenths of" this difference is the product of and this, or

This is equal to forty, so write the equation as

### Example Question #1 : Solving Linear Equations In Word Problems

Write as an equation:

Twice the sum of a number and ten is equal to the difference of the number and one half.

**Possible Answers:**

**Correct answer:**

Let represent the unknown number.

"The sum of a number and ten" is the expression . "Twice" this sum is two times this expression, or

.

"The difference of the number and one half" is a subtraction of the two, or

Set these equal, and the desired equation is

### Example Question #2 : Solving Linear Equations In Word Problems

If a rectangle possesses a width of and has a perimeter of , then what is the length?

**Possible Answers:**

**Correct answer:**

In order to solve this problem, we need to recall the formula for perimeter of a rectangle:

We can substitute in our known values and solve for our unknown variable (i.e. length):

We want to isolate the to one side of the equation. In order to do this, we will first subtract from both sides of the equation.

Next, we can divide each side by

The length of the rectangle is

### Example Question #2 : Solving Linear Equations In Word Problems

If a rectangle possesses a width of and has a perimeter of , then what is the length?

**Possible Answers:**

**Correct answer:**

In order to solve this problem, we need to recall the formula for perimeter of a rectangle:

We can substitute in our known values and solve for our unknown variable (i.e. length):

We want to isolate the to one side of the equation. In order to do this, we will first subtract from both sides of the equation.

Next, we can divide each side by

The length of the rectangle is

### Example Question #1 : Solving Linear Equations In Word Problems

If a rectangle possesses a width of and has a perimeter of , then what is the length?

**Possible Answers:**

**Correct answer:**

In order to solve this problem, we need to recall the formula for perimeter of a rectangle:

We can substitute in our known values and solve for our unknown variable (i.e. length):

We want to isolate the to one side of the equation. In order to do this, we will first subtract from both sides of the equation.

Next, we can divide each side by

The length of the rectangle is

### Example Question #4 : Solving Linear Equations In Word Problems

If a rectangle possesses a width of and has a perimeter of , then what is the length?

**Possible Answers:**

**Correct answer:**

In order to solve this problem, we need to recall the formula for perimeter of a rectangle:

We can substitute in our known values and solve for our unknown variable (i.e. length):

Next, we can divide each side by

The length of the rectangle is