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

## Example Questions

### Example Question #51 : How To Find The Solution To An Equation

Explanation:

To find the sum of H and J, it is necessary to first find the value of H and J. The value of H can be found by isolating the variable in the first equation provided (i.e. by dividing both sides of the equal sign by 2). Use a similar method to find the value of J.

Substitute the found values of J and H into the equation to find the answer.

### Example Question #52 : How To Find The Solution To An Equation

When a certain number is multiplied by 6, the product is 54. If the same number is added to 6, then the sum is which of the following?

Explanation:

To determine what the sum will be, one must first determine what the number is. The initial information can be converted into an equation using the variable n for the unknown number. Isolate the variable and simplify as needed to determine what its value is.

•

Once the value of n is known, add the 6 to number. This will be the sum.

The sum is 15.

### Example Question #51 : Equations

The product of is the same as the sum of  and what number?

Explanation:

To answer this question, first determine what the product of the three numbers is

Then convert the last phrase to an equation then solve.

### Example Question #51 : Ssat Middle Level Quantitative (Math)

Solve for n.

Explanation:

The first step is to clear the term in the parantheses:

Then combine terms on each side of the equations:

Subract 6 on both sides of the equation:

Now add 5n to both sides:

### Example Question #52 : Equations

Find the value of the variable .

Explanation:

First step to this problem is to subtract

Then simply add 32 to both sides of the equation to isolate the variable x.

### Example Question #53 : Equations

Solve for  in the following equation,

.

Explanation:

The first step is to get rid of the fraction by multipling both sides by .

This leaves you with .

Then you must get all of the  variables on one side by adding  to both sides resulting in .

Finally get  by itself by dividing both sides by  leaving you with the answer of .

### Example Question #54 : Equations

Find the length of a rectangle with an area of  and width of

Explanation:

In order to solve for the length of the rectangle given the area, we must remember the area formula for the area of a rectangle.

Note: The * means multiply.

We know the area is 42, so we substitute 42 for area.

We also know the width is 7, so we substitute 7 for the width.

In order to determine the length, we must divide both sides by 7.

On the left side we find that  and on the right side we find that the 7's cancel to give us:

### Example Question #51 : Algebra

Your friend buys a pack of gummy bears at the concession stand to share equally with you and the four additional friends you plan to meet up with inside the movie theater. Which of the following CANNOT be the number of gummy bears in the package?

Explanation:

The key to solving this question is to understand that in order for the gummy bears to be shared equally among the 6 friends, the number of gummy bears must be divisible by 6. The question asks for which one cannot be the answer, which is 32 as it is the only one not divisible by 6.

### Example Question #1 : Use Variables To Represent Numbers And Write Expressions: Ccss.Math.Content.6.Ee.B.6

A barista has to make sixty pounds of a special blend of coffee at Moonbucks, using Hazelnut Happiness beans and Pecan Delight beans. If there are fourteen fewer pounds of Hazelnut Happiness beans in the mixture than Pecan Delight beans, then how many pounds of each will she use?

If  represents the number of pounds of Pecan Delight coffee beans in the mixture, then which of the following equations could be set up in order to find the number of pounds of each variety of bean?

Explanation:

Since there are fourteen fewer pounds of Hazelnut Happiness beans in the mixture than Pecan Delight beans , then the number of pounds of Hazelnut Happiness beans is fourteen subtracted from :

.

Add the number of pounds of Pecan Delight beans, , to the number of pounds of Hazelnut Happiness beans, , to get the number of pounds of the mixture, which is .

This translates to the following equation:

### Example Question #121 : Word Problems

A barista has to make forty pounds of a special blend of coffee at Moonbucks, using Vanilla Dream beans and Strawberry Heaven beans. If there are twelve more pounds of Vanilla Dream beans in the mixture than Strawberry Heaven beans, then how many pounds of each will she use?

If  represents the number of pounds of Strawberry Heaven coffee beans in the mixture, then which of the following equations could be set up in order to find the number of pounds of each variety of bean?