### All SAT Mathematics Resources

## Example Questions

### Example Question #1 : Extrapolating Linear Proportions

You are planning a party. The maximum number of people the reception hall can hold is person for every square feet of space. If the hall is feet wide and feet long, how many people can you invite?

**Possible Answers:**

**Correct answer:**

Total area of hall

At person per square feet, per person = people

### Example Question #2 : Extrapolating Linear Proportions

A cafeteria with tables can sit people. Some tables can sit people and some can sit people. What is the ratio of the number of -person tables to the number of -person tables?

**Possible Answers:**

**Correct answer:**

Let be the number of -person tables, and be the number of -person tables. Since there are tables in the cafeteria, . * *represents the number of people sitting at -person tables, and * *represents the number of people sitting at -person tables. Since the cafeteria can seat people, . Now we have equations and unknowns, and can solve the system. To do this, multiply the first equation by and subtract it from the second equation. This yields ; solving for tells us there are tables that seat people. Since , , so there are tables that seat people. The ratio of is therefore .

### Example Question #2 : Extrapolating Linear Proportions

A mile is feet. Susan is able to walk a fast pace of miles per hour. How many feet will she walk in minutes?

**Possible Answers:**

**Correct answer:**

Calculate the number of feet walked in an hour. Then calculate what fraction of an hour minutes is.

feet walked in an hour

minutes in an hour, so minutes = hour

feet walked in minutes

### Example Question #4 : Extrapolating Linear Proportions

A bag contains marbles that are either red, blue, or green. The ratio of red to blue to green marbles is . If one-third of the red marbles and two-thirds of the green marbles are removed, what fraction of the remaining marbles in the bag will be blue?

**Possible Answers:**

**Correct answer:**

First, we need to figure out how many red, blue, and green marbles are in the bag before any are removed. Let represent the number of red marbles. Because the marbles are in a ratio of , then if there are red marbles, there are blue, and green marbles. If we add up all of the marbles, we will get the total number of marbles, which is .

Because the number of red marbles is , there are , or red marbles. There are , or blue marbles, and there are , or green marbles.

So, the bag originally contains red, blue, and green marbles. We are then told that one-third of the red marbles is removed. Because one-third of is , there would be red marbles remaining. Next, two-thirds of the green marbles are removed. Because , there would be green marbles left after are removed.

To summarize, after the marbles are removed, there are red, 60 blue, and green marbles. The question asks us for the fraction of blue marbles in the bag after the marbles are removed. This means there would be blue marbles out of the left in the bag. The fraction of blue marbles would therefore be , which simplifies to .

The answer is .

### Example Question #5 : Extrapolating Linear Proportions

Tom wants to buy an aquarium. He has found that he needs one filter for the aquarium for every creatures or plants he puts in the tank. The fish he wants to get also requires special plants be present at plants for every fish. These plants need cleaning fish for every plants in order to flourish.

If Tom is going to buy filters, how many of the original fish he wanted will his aquarium support?

**Possible Answers:**

**Correct answer:**

filters can support a total of creatures/plants. The fish he wants need plants for every fish. The plant needs cleaning fish per plants. Thus for every of the fish he wants, he needs plants and cleaning fish.

This gives us a total of creatures. We can complete this number times, but then we are left with spots open that the filters can support.

This is where the trick arises. We can actually add one more fish in. Since plant supports up to fish , and 2 cleaning fish support up to plants, we can add fish, plant, and cleaning fish to get a total of creatures. If we attempt to add fish, then we must also add the plant, but then we don't have enough space left to add the cleaning fish necessary to support the remaining plant.

Thus, Tom can buy at most of the fish he originally wanted to get.

### Example Question #1 : Extrapolating Linear Proportions

In the reptile house at the zoo, the ratio of snakes to lizards is to . After the zoo adds more snakes to the exhibit, the ratio changes to to . How many lizards are in the reptile house?

**Possible Answers:**

**Correct answer:**

In order to maintain a proportion, each value in the ratio must be multiplied by the same value:

Before and after the snakes arrive, the number of lizards stays constant.

Before new snakes — Snakes : Lizards =

After new snakes — Snakes : Lizards =

Before the new snakes arrive, there are snakes. After the snakes are added, there are snakes. Therefore, . Solving for gives .

There are lizards, or lizards.

### Example Question #4 : Extrapolating Linear Proportions

A small company's workforce consists of store employees, store managers, and corporate managers in the ratio . How many employees are either corporate managers or store managers if the company has a total of employees?

**Possible Answers:**

**Correct answer:**

Let be the number of store employees, the number of store managers, and the number of corporate managers.

, so the number of store employees is .

, so the number of store managers is .

, so the number of corporate managers is .

Therefore, the number of employees who are either store managers or corporate managers is .

### Example Question #2 : Extrapolating Linear Proportions

The exchange rate in some prehistoric village was jagged rocks for every smooth pebbles. Also, one shiny rock could be traded for smooth pebbles. If Joaquin had jagged rocks, what is the maximum number of shiny rocks he could trade for?

**Possible Answers:**

**Correct answer:**

We can use dimensional analysis to solve this problem. We will create ratios from the conversions given.

Since Joaquin cannot trade for part of a shiny rock, the most he can get is shiny rocks.

### Example Question #3 : Extrapolating Linear Proportions

In a flower bed, Joaquin plants Begonias for every Zinnias, and Marigolds for every Begonias. What is the ratio of Marigolds to Zinnias planted in the flower bed?

**Possible Answers:**

**Correct answer:**

First, we should write a fraction for each ratio given:

Next, we will multiply these fractions by each other in such a way that will leave us with a fraction that has only Z and M, since we want a ratio of these two flowers only.

So the final answer is

### Example Question #4 : Extrapolating Linear Proportions

A lawn can be mowed by people in hours. If people take the day off and do not help mow the grass, how many hours will it take to mow the lawn?

**Possible Answers:**

**Correct answer:**

The number of hours required to mow the lawn remains constant and can be found by taking the original workers times the hours they worked, totaling hours. We then split the total required hours between the works that remain, and each of them have to work and hours: .