Basic Math - Basic Arithmetic

A city bus has five stops left on its route. At the first stop, people get off. At the second stop, get off. At the third, no one gets off. At the fourth, people get off. At the fifth, there are people left on the bus, and they all get off. How many people were on the bus before the first stop?

Explanation

To solve, create a linear equation:

represents the total number of people on the bus before the first stop.

We then subtract the amount of people that got off at each stop and set that equal to the number of people to get off at the final stop.

Multiply:

$\frac{5}{6}\times\frac{12}{25}=?$

$\frac{2}{5}$

$\frac{60}{100}$

$\frac{1}{75}$

Explanation

Multiply the numerators together, then multiply the denominators together.

$\frac{5}{6}\times\frac{12}{25}=\frac{5 \times 12}{6\times25}=\frac{60}{150}$

To simplfy we can pull out a from the numerator and denominator, thus canceling them. The following answer is the result:

$=\frac{30\cdot2}{30\cdot5}=\frac{2}{5}$

Explanation

To solve, create a linear equation:

represents the total number of people on the bus before the first stop.

We then subtract the amount of people that got off at each stop and set that equal to the number of people to get off at the final stop.

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.

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:

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

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:

Multiply:

$\frac{5}{6}\times\frac{12}{25}=?$

$\frac{2}{5}$

$\frac{60}{100}$

$\frac{1}{75}$

Explanation

Multiply the numerators together, then multiply the denominators together.

$\frac{5}{6}\times\frac{12}{25}=\frac{5 \times 12}{6\times25}=\frac{60}{150}$

To simplfy we can pull out a from the numerator and denominator, thus canceling them. The following answer is the result:

$=\frac{30\cdot2}{30\cdot5}=\frac{2}{5}$

Multiply:

$\frac{5}{6}\times\frac{12}{25}=?$

$\frac{2}{5}$

$\frac{60}{100}$

$\frac{1}{75}$

Explanation

Multiply the numerators together, then multiply the denominators together.

$\frac{5}{6}\times\frac{12}{25}=\frac{5 \times 12}{6\times25}=\frac{60}{150}$

To simplfy we can pull out a from the numerator and denominator, thus canceling them. The following answer is the result:

$=\frac{30\cdot2}{30\cdot5}=\frac{2}{5}$

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

To solve, create a linear equation:

represents the total number of people on the bus before the first stop.

We then subtract the amount of people that got off at each stop and set that equal to the number of people to get off at the final stop.

Basic Arithmetic

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