# SSAT Middle Level Math : How to find the solution to an equation

## Example Questions

### Example Question #41 : How To Find The Solution To An Equation

Solve for :

Explanation:

Add 2 to both sides of the inequality:

Divide both sides by 4:

### Example Question #42 : How To Find The Solution To An Equation

If , then what is the value of

Explanation:

To solve for the equation, , we add 7 to each side. By doing this, we can see that y is equal to 19.

Thus, in the equation , we plug in 19 for y.

Thus, 15 is he correct answer.

### Example Question #43 : How To Find The Solution To An Equation

Marcia is four times as old as her daughter Janice. In twelve years, Janice will be 20 years old. In how many years will Marcia be three times as old as Janice?

Explanation:

Janice will be 20 years old in 12 years, so she is  years old now. Marcia is four times as old, or  years old.

Let  be the number of years in which Marcia's age will be three times Janice's age. Janice will be  years old, and Marcia will be  years old. Since Marcia will be three times as old as Janice, we can set up and solve the equation:

### Example Question #44 : How To Find The Solution To An Equation

Twenty added to one-fourth of a number is equal to fifty-six. What is the number?

The correct answer is not among the other choices.

Explanation:

If we let  be the number, "one-fourth of a number" can be written as

.

"Twenty added to one-fourth of a number" can be written as

.

Set this equal to fifty-six and solve for :

### Example Question #45 : How To Find The Solution To An Equation

Which of the following phrases can be written as the algebraic expression ?

The correct answer is not given among the other responses.

The difference of a number and seven multiplied by ninety-nine

Ninety-nine decreased by the product of seven and a number

The difference of seven and a number multiplied by ninety-nine

The product of seven and a number decreased by ninety-nine

Ninety-nine decreased by the product of seven and a number

Explanation:

is ninety-nine decreased by

is the product of seven and a number.

Therefore, the  is "ninety-nine decreased by the product of seven and a number".

### Example Question #46 : How To Find The Solution To An Equation

Fifty-four subtracted from one-sixth of a number is equal to twelve. What is the number?

Explanation:

If we let  be the unknown number, "one-sixth of a number" can be written as

.

"Fifty-four subtracted from one-sixth of a number" can be written as

.

Set this equal to twelve, and solve for :

### Example Question #47 : How To Find The Solution To An Equation

Which of the following phrases can be written as the algebraic expression ?

The product of nine and a number subtracted from eighty-six

Nine mutiplied by the difference of a number and eighty-six

Eighty-six subtracted from the product of nine and a number

The correct answer is not given among the other responses.

Nine mutiplied by the difference of eighty-six and a number

Nine mutiplied by the difference of eighty-six and a number

Explanation:

is nine multiplied by the expression .

is the difference of eighty-six and a number.

Subsequently,  is "nine multiplied by the difference of eighty-six and a number".

### Example Question #48 : How To Find The Solution To An Equation

Which of the following phrases can be written as the algebraic expression  ?

The difference of a number and three added to seventy-six

The sum of a number and three subtracted from seventy-six

Seventy-six subtracted from the sum of a number and three

The correct answer is not given among the other responses.

The difference of three and a number added to seventy-six

The sum of a number and three subtracted from seventy-six

Explanation:

is  subtracted from seventy-six.

is the sum of a number () and three.

Therefore,

is "the sum of a number and three subtracted from seventy-six".

### Example Question #49 : How To Find The Solution To An Equation

You must first use the distributive property to solve this problem.

Find the value of the variable

Explanation:

First distribute the 3 over to the terms inside the parantheses. You should get the following value

Second subtract 12 on both sides of the equation,

Then isolate the variable "a" by dividing both sides by 3,

You can check your answer by inserting 4 into the original equation and solve the equation.

### Example Question #50 : How To Find The Solution To An Equation

A mother takes her three children to the doctor for their yearly checkup. During the checkup, the nurse asks to see the children in order of increasing age. Based on the following information, which child will the nurse see first?

• Zach and Paul have combined ages of 15.
• Paul and Anna have combined ages of 16.
• Anna and Zach have combined ages of 17.

All three children are the same age.

Anna

Paul

Zach

Paul

Explanation:

Based on the information provided in the question, the nurse will see the youngest child first. To determine which child is youngest, the ages of all children must be found. The three lines of information can be converted to equations using Z = Zach, P = Paul, and A = Anna.

Isolate Z in the first equation by subtracting P from both sides of the equal sign. Use the newly found relationship in equation 3 and simplify as necessary.

A or P can be isolated, similar to above, as both variables appear in equation 2. Plug the isolated equation in equation 2 and again simplify as necessary. For this explanation A has been solved for.

This means that Paul is 7 years old. Plug this information into the original equation.

So, Paul is 7 years old, Zach is 8 years old, and Anna is 9 years old; therefore, Paul will be seen by the nurse first.