Ratios and Rates

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Basic Math › Ratios and Rates

Questions 1 - 10

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:

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

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.

Explanation

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.

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?

Explanation

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:

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:

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

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.

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?

Explanation

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:

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

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:

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

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.

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

Explanation

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.

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

Explanation

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 .

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

Explanation

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.

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

Explanation

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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