# Basic Arithmetic : Ratios and Rates

## Example Questions

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### 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?

Explanation:

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?

Explanation:

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?

Explanation:

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?

Explanation:

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

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: Explanation: 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?

There is not enough information to answer the question.

Explanation:

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: Explanation: 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?