# New SAT Math - Calculator : Solving Linear Equations in Word Problems

## Example Questions

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### 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?

Explanation:

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."

Explanation:

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.

Explanation:

"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.

Explanation:

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?

Explanation:

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?

Explanation:

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?

Explanation:

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?

Explanation:

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 #5 : Solving Linear Equations In Word Problems

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

Explanation:

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 #6 : Solving Linear Equations In Word Problems

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

Explanation:

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

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