Ratios and Rates - Basic Arithmetic

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Question

I put in a bank account at a annual simple interest rate. How much interest will have accumulated after two years?

Answer

This is a simple interest rate problem, for which we use the formula:

Interest = P x r x t

P is the principal, or original loan amount; r is the annual interest rate; and t is the number of years in question.

In this problem, P = $9,000; r = 4%; and t = 2 years. Plugging these into the formula gives us:

$Interest=9,000\times \frac{4}{100}\times 2$

So, after two years the account has gathered $720 in interest.

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Question

If one recipe calls for eggs to make waffles, how many eggs are needed to make waffles?

Answer

To solve this problem, we can set up a proportion.

$\frac{\text{eggs}}{\text{waffles}}=\frac{\text{eggs}}{\text{waffles}}$

That proportion will tell us how many eggs go into each waffle. Since the number of eggs that goes into each waffle doesn't change, we can set these two proportions equal to each other.

Now, fill it in with the information we know:

$\frac{\text{6 eggs}}{\text{18 waffles}}=\frac{\text{x eggs}}{\text{30 waffles}}$

For the sake of making math easier, drop the words so we get the following equation:

$\frac{6}{18}=\frac{x}{30}$

To solve for x, cross-multiply this equation.

Divide both sides by 18.

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Question

The ratio of boys to girls in a class is . If there are boys in the class, how many girls are in the class?

Answer

We can write the following equation using the ratios given:

$\frac{3}{5}=\frac{12}{x}$

is the number of girls in the class.

Now, we can cross multiply to get the following equation:

Now divide both sides by .

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Question

If painters can paint houses in day, how many painters would it take to paint houses in day?

Answer

We can set up the following proportions using the given information:

$\frac{8\text{ painters}}{16\text{ houses}}=\frac{x\text{ painters}}{58\text{ houses}}$

Now, cross multiply these two fractions to get the following equation:

Divide both sides by .

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Question

If a car travels at miles per hour, how many hours would it take the car to travel miles?

Answer

We can write 40 miles per hour as the following fraction:

$\frac{40\text{ miles}}{1\text{ hour}}$

Since we want to figure out how many hours it takes a car to travel 200 miles, we can write the following equation:

$\frac{40\text{ miles}}{1\text{ hour}}=\frac{200\text{ miles}}{x\text{ hours}}$

Now, cross multiply.

Divide both sides by 40.

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Question

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?

Answer

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

$\frac{10 seconds}{1gallon}$

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

$\frac{10seconds}{1gallon} \times 400 gallons = 4000 seconds$

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

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Question

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?

Answer

The team has won 5 games.

The number of played games is 25.

Therefore, the ratio of winnings to the total is:

$\frac{5}{25}=\frac{1}{5}$

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Question

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

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:

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Question

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

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:

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Question

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?

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:

$\frac{7}{100}\times 35=2.45$

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

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Question

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?

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:

$\frac{15}{100}\times 20,000=3,000$

Joe made $3,000 from commission yesterday.

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Question

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?

Answer

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

$6\times 200=1,200$

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

$\frac{6}{100}\times 1,200=72$

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:

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Question

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

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:

$150=\frac{8}{100}\times x$

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

$150\times 100=8x$

$\frac{15,000}{8}=x$

Maggie's sale was $1,875.

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Question

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.

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:

$120=\frac{x}{100}\times 670$

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

$120\times 100=x\times 670$

$\frac{12,000}{670}=x$

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

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Question

Find the value of in the following ratio table:

Answer

The numbers on the left side to the numbers on the right side are in a ratio of 1 to 7. In other words, multiply the numbers on the left by 7 to get the numbers on the right.

Using that ratio, we arrive at the following equation for x:

Now, divide both sides by 7.

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Question

Find the value of in the ratio table above.

Answer

To find the multiplier, divide two numbers from the same row:

$12\div2=6$

Now, multiply this by and set that equal to

Divide both sides by

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Question

In the ratio table above, find .

Answer

To figure out the ratio, divide the second column by the first.

$7\div49=\frac{1}{7}$

Since we are multiplying the first column by $\frac{1}{7}$ to get the second column, we can set up the following equation for .

$\frac{1}{7}x=12$

Multiply both sides by 7.

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Question

Find the value of in the ratio table above.

Answer

To find , we can set up the following ratio:

$\frac{12}{8}=\frac{9}{x}$

Now, cross multiply and solve.

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Question

Find the value of in the ratio table above.

Answer

To find , we can set up the following ratios:

$\frac{6}{24}=\frac{9}{x}$

Now, cross-multiply and solve.

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Question

How many minutes are in a hours?

Answer

Knowing that there are 60 minutes in an hour, multiply that amount by the total number of hours (3.5):

$60 \times 3.5= 210$ minutes

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