# SSAT Upper Level Math : Proportion / Ratio / Rate

## Example Questions

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### Example Question #61 : Number Concepts And Operations

A barn has  geese,  ducks, and  chickens. What is the ratio of geese to chickens?

Explanation:

First, add up the total number of ducks, geese, and chickens.

Now, write the fraction of these animals that are geese and the fraction of these animals that are chickens.

Now, since we want the ratio of geese to chickens, we write the fractions as thus:

Divide and simplify the resulting fraction to find the ratio.

### Example Question #62 : Number Concepts And Operations

If  pounds of chicken cost , how much does  pounds of chicken cost?

Explanation:

There is more than one way to solve this problem. You can either figure out how much the chicken costs per pound and multiply that cost by three pounds, or you can set up a proportion and solve for the cost of three pounds of chicken that way.

1) Solving the Problem Using Cost per Pound

First, find how much the chicken costs per pound.

Since chicken costs  per pound, multiply this by the number of pounds we need to get the cost.

pounds of chicken cost .

2) Solving the Problem Using a Proportion

You can set up a proportion to figure out how much  pounds of chicken costs:

Cross multiply:

Solve for , the cost of  pounds of chicken:

### Example Question #63 : Number Concepts And Operations

In a class of  students, the ratio of freshmen to sophomores to juniors is . How many juniors are in the class?

Explanation:

Let  be the number of freshmen,  be the number of sophomores, and  be the number of juniors.

Now, since we have  students,

Since we want to find the number of juniors, we need to find the value of .

### Example Question #1 : Rational Numbers

In a zoo with  animals, the ratio of mammals to reptiles to birds is . How many birds does the zoo have?

Explanation:

Let  be the number of mammals, be the number of reptiles, and  be the number of birds.

Since the zoo has  animals,

Because we want the number of birds, we need to find the value of .

### Example Question #65 : Number Concepts And Operations

In a high school of  students, the ratio of freshmen to sophomores to juniors to seniors is . How many juniors does this high school have?

Explanation:

Let  be the number of freshmen,  be the number of sophomores,  be the number of juniors, and  be the number of seniors.

Because the high school has  students,

Since we want to find out how many juniors there are, we need the value of .

### Example Question #66 : Number Concepts And Operations

In a high school, the ratio of freshmen to seniors is . If there are  seniors, how many freshmen are there?

Explanation:

Set up the following proportion, with  being the number of freshmen.

Now, cross-multiply and solve for .

### Example Question #67 : Number Concepts And Operations

On a beach, the ratio of crabs to seagulls is . If there are  crabs and seagulls on the beach, how many crabs are there?

Explanation:

Let  be the number of crabs and  be the number of seagulls.

Since there are  crabs and seagulls on the beach,

Because the question asks for the number of crabs, we need to find the value of .

### Example Question #1 : Proportion / Ratio / Rate

There are  boys and  girls at a playground. What is the ratio of boys to girls?

Explanation:

Write the numbers of boys and girls as a fraction, then simplify.

can also be written as

### Example Question #1 : Fractions

At a high school, there are  freshmen,  sophomores,  juniors, and  seniors. What is the ratio of seniors to freshmen?

to

to

to

to

to

Explanation:

Write the number of seniors and numbers of freshmen as a fraction:

That fraction is equivalent to .

### Example Question #70 : Number Concepts And Operations

The angles in a triangle are in the ratio . What is the angle measurement of the largest angle?