### All SSAT Upper Level Math Resources

## Example Questions

### Example Question #1 : How To Find A Ratio

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

**Possible Answers:**

**Correct answer:**

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 #1 : Rational Numbers

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

**Possible Answers:**

**Correct answer:**

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 #1 : Rational Numbers

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

**Possible Answers:**

**Correct answer:**

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 : Decide If Two Quantiies Are In A Proportional Relationship: Ccss.Math.Content.7.Rp.A.2a

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

**Possible Answers:**

**Correct answer:**

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 #2 : Rational Numbers

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?

**Possible Answers:**

**Correct answer:**

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 #2 : Rational Numbers

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

**Possible Answers:**

**Correct answer:**

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

Now, cross-multiply and solve for .

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

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

**Possible Answers:**

**Correct answer:**

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 #3 : How To Find A Ratio

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

**Possible Answers:**

**Correct answer:**

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

can also be written as

### Example Question #3 : Rational Numbers

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

**Possible Answers:**

to

to

to

to

**Correct answer:**

to

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

That fraction is equivalent to .

### Example Question #3 : Rational Numbers

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

**Possible Answers:**

**Correct answer:**

Let be the values of the angles.

Since all the angles in a triangle need to add up to ,

Because we want the value of the largest angle, we need to find the value of .