# SSAT Middle Level Math : Numbers and Operations

## Example Questions

### Example Question #21 : Ratio And Proportion

Phil invites sixty friends from his current school, thirty-five of whom are girls, to his birthday party; he also invites his two female cousins. Phil wants the ratio of girls to boys at the party to be two to one, so he decides to also invite some girls from his old school. How many new girls will he need to invite, assuming he does not invite anyone else?

Explanation:

So far, there are 37 girls - 35 classmates and 2 cousins - and 26 boys - 25 classmates and Mike himself. For the ratio of girls to boys to be 2 to 1, the number of girls must be twice the number of boys, or  girls. Mike will need  more girls.

### Example Question #1 : Compute Unit Rates Associated With Ratios Of Fractions: Ccss.Math.Content.7.Rp.A.1

Write as a unit rate:  revolutions in  minutes

revolutions per minute

revolutions per minute

revolutions per minute

revolutions per minute

revolutions per minute

revolutions per minute

Explanation:

Divide the number of revolutions by the number of minutes to get revolutions per minute:

,

making  revolutions per minute the correct choice.

### Example Question #1 : Understand The Concept Of A Ratio: Ccss.Math.Content.6.Rp.A.1

If candidate A receives  vote for every  votes that candidate B receives. At the end of the election candidate B has  votes. How many votes did candidate A get?

Explanation:

In order to solve this problem we need to create a ratio with the given information. It says that for every  vote cast for candidate A, candidate B got  votes. We can write the following ratio.

Now substitute in the given numbers.

We know that candidate B received  votes. Write a new ratio.

Now, use the original relationship to create a proportion and solve for the number of votes that candidate A received.

Cross multiply and solve for .

Simplify.

Divide both sides of the equation by .

Solve.

### Example Question #1 : Understand The Concept Of A Ratio: Ccss.Math.Content.6.Rp.A.1

If candidate A receives  votes for every  votes that candidate B receives. At the end of the election candidate B has  votes. How many votes did candidate A get?

Explanation:

In order to solve this problem we need to create a ratio with the given information. It says that for every  votes cast for candidate A, candidate B got  votes. We can write the following ratio.

Now substitute in the given numbers.

We know that candidate B received  votes. Write a new ratio.

Now, use the original relationship to create a proportion and solve for the number of votes that candidate A received.

Cross multiply and solve for .

Simplify.

Divide both sides of the equation by .

Solve.

### Example Question #1 : Ratios & Proportional Relationships

If candidate A receives  vote for every  votes that candidate B receives. At the end of the election candidate B has  votes. How many votes did candidate A get?

Explanation:

In order to solve this problem we need to create a ratio with the given information. It says that for every  vote cast for candidate A, candidate B got  votes. We can write the following ratio.

Now substitute in the given numbers.

We know that candidate B received  votes. Write a new ratio.

Now, use the original relationship to create a proportion and solve for the number of votes that candidate A received.

Cross multiply and solve for .

Simplify.

Divide both sides of the equation by .

Solve.

### Example Question #24 : Ratio And Proportion

If candidate A receives  votes for every  votes that candidate B receives. At the end of the election candidate B has  votes. How many votes did candidate A get?

Explanation:

In order to solve this problem we need to create a ratio with the given information. It says that for every  votes cast for candidate A, candidate B got  votes. We can write the following ratio.

Now substitute in the given numbers.

We know that candidate B received  votes. Write a new ratio.

Now, use the original relationship to create a proportion and solve for the number of votes that candidate A received.

Cross multiply and solve for .

Simplify.

Divide both sides of the equation by .

Solve.

### Example Question #21 : How To Find A Ratio

If candidate A receives  votes for every  votes that candidate B receives. At the end of the election candidate B has  votes. How many votes did candidate A get?

Explanation:

In order to solve this problem we need to create a ratio with the given information. It says that for every  votes cast for candidate A, candidate B got  votes. We can write the following ratio.

Now substitute in the given numbers.

Reduce.

We know that candidate B received  votes. Write a new ratio.

Now, use the original relationship to create a proportion and solve for the number of votes that candidate A received.

Cross multiply and solve for .

Simplify.

Divide both sides of the equation by .

Solve.

### Example Question #1 : Ratios & Proportional Relationships

If candidate A receives  vote for every  votes that candidate B receives. At the end of the election candidate B has  votes. How many votes did candidate A get?

Explanation:

In order to solve this problem we need to create a ratio with the given information. It says that for every  vote cast for candidate A, candidate B got  votes. We can write the following ratio.

Now substitute in the given numbers.

We know that candidate B received  votes. Write a new ratio.

Now, use the original relationship to create a proportion and solve for the number of votes that candidate A received.

Cross multiply and solve for .

Simplify.

Divide both sides of the equation by .

Solve.

### Example Question #1 : Understand The Concept Of A Ratio: Ccss.Math.Content.6.Rp.A.1

If candidate A receives  votes for every  votes that candidate B receives. At the end of the election candidate B has  votes. How many votes did candidate A get?

Explanation:

In order to solve this problem we need to create a ratio with the given information. It says that for every  votes cast for candidate A, candidate B got  votes. We can write the following ratio.

Now substitute in the given numbers.

We know that candidate B received  votes. Write a new ratio.

Now, use the original relationship to create a proportion and solve for the number of votes that candidate A received.

Cross multiply and solve for .

Simplify.

Divide both sides of the equation by .

Solve.

### Example Question #22 : How To Find A Ratio

If candidate A receives  votes for every  vote that candidate B receives. At the end of the election candidate B has  votes. How many votes did candidate A get?

Explanation:

In order to solve this problem we need to create a ratio with the given information. It says that for every  votes cast for candidate A, candidate B got  vote. We can write the following ratio.

Now substitute in the given numbers.

We know that candidate B received  votes. Write a new ratio.

Now, use the original relationship to create a proportion and solve for the number of votes that candidate A received.

Cross multiply and solve for .

Simplify and solve.