### All Basic Arithmetic Resources

## Example Questions

### Example Question #2 : Linear Equations With Ratios And Rates

Jessica fills an aquarium with water. The aquarium can hold gallons of water—it's a huge aquarium! The faucet fills the tank at a rate of 1 gallon every 10 seconds. How long (in seconds) will it take Jessica to fill the tank?

**Possible Answers:**

**Correct answer:**

The rate at which Jessica fills the tank can be written as a ratio:

Multiply this ratio by the total amount of gallons possible to get the amount of time it takes to fill the tank.

Gallon units cancel out, so you are left with seconds as the final unit in the answer.

### Example Question #1 : Other Ratios And Rates

A diving team swims in competitions, and wins overall competitions. What is their lose to win ratio?

**Possible Answers:**

**Correct answer:**

A diving team that wins 6 competitions out of 10 will have 6 winning meets and 4 losing meets. Therefore, their lose to win ratio is:

This can be reduced to:

### Example Question #1 : Other Ratios And Rates

A soccer team wins out of their games. What is their win to loss ratio?

**Possible Answers:**

**Correct answer:**

Since the soccer team has won 8 out of 10 games, they have 8 winning games and 2 losing games.

Therefore, their win to loss ratio is:

This ratio can be reduced to:

### Example Question #2 : Other Ratios And Rates

The sales tax rate at your favorite clothing store is . You buy a shirt for and a hat for . What is the total amount, including tax, that you pay for your purchases?

**Possible Answers:**

**Correct answer:**

First, you want to figure out the total cost of your purchase by adding up the price of all the items you are buying:

Then, you find the tax you will pay on this total by taking 7% of $35:

You add the cost of your purchase plus the tax to find the total amount that you have to pay:

### Example Question #3 : Other Ratios And Rates

Joe takes home a commission of his total sales at the furniture store. Yesterday he sold one chair and two chairs. How much money did he make from commission yesterday?

**Possible Answers:**

**Correct answer:**

First you find the total amount of sales that Joe made yesterday by adding the cost of each item he sold:

Joe sold $20,000 worth of furniture yesterday. He makes 15% commision, so we find 15% of 20,000:

Joe made $3,000 from commission yesterday.

### Example Question #4 : Other Ratios And Rates

Sara has a weekly salary of . This week she sells six lamps and takes of those sales as her commission. What is the total amount of money she makes this week?

**Possible Answers:**

**Correct answer:**

First you find the total amount of sales that Sara made this week by selling six lamps at $200 a piece:

Sara gets a 6% commission on her sales, so next you find what 6% of 1,200 is:

So, Sara makes $72 from commission this week. However, we can't forget about the $500 weekly salary she also gets! We add her week's commission plus weekly salary to find the total amount she makes during this particular week:

### Example Question #2 : Other Ratios And Rates

Maggie works on an commission rate. After one great sale, she makes from commission alone. How much was the sale?

**Possible Answers:**

There is not enough information to answer the question.

**Correct answer:**

We can interpret the information given in the question as "150 is 8% of some number, or whatever amount Maggie's sale is." We can turn this sentence into algebra by calling "some number" x:

From here, we solve for x by isolating it on one side of the equation:

Maggie's sale was $1,875.

### Example Question #2 : Other Ratios And Rates

Waitress Kelly sold worth of food to her tables on Saturay night. If she made in tips that night, what was her overall tip percentage? Round your final answer to the nearest tenth.

**Possible Answers:**

**Correct answer:**

From the information given in the question, we can ask ourselves the following question- $120 is what percent of $670? We can turn this into algebra by calling "what number" x:

From here, we solve for x by isolating it on the right side of the equation:

Rounding to the nearest tenth gives us 17.9, so the final answer is 17.9%.

### Example Question #2 : Other Ratios And Rates

In a football game, a team won out of the games they played. What is the ratio of their wins to their total number of games played?

**Possible Answers:**

**Correct answer:**

The team has won 5 games.

The number of played games is 25.

Therefore, the ratio of winnings to the total is: