Question

A garage mechanic purchases oil in a 40-gallon container for changing oil in customers' cars. After 22 oil changes requiring 4 qt each, how much oil, in quarts, is left in the 40-gallon container?

Answer 1

The mechanic has a 40-gallon oil container for changing oil in customer's cars.

Each time he changes the oil of a car, he spends 4qt oil.

You need to determine how much oil is left in the container after 22 oil changes.

To determine how much oil is left, considering that you have to express the result in quarts, the first step is to express the total amount of oil in the container in quarts.

1 gallon is equal to 4 quarts, to determine how many quarts represent 40 gallons, you have to apply cross multiplication:

1 gallon → 4 quarts

40 gallons → x quarts

Both relationships are in the same proportion so that:

`\begin{gathered} (4)/(1)=(x)/(40) \\ 4=(x)/(40)→multiply\text{ }by\text{ }40 \\ 40*4=x \\ x=160qt \end{gathered}`

The total amount of oil in the container is 160 quarts.

The next step is to calculate how much oil was spent in the 22 oil changes.

You know that the mechanic uses 4 quarts for each oil change, if you multiply the amount of oil used in each change by the number of oil changes he performed, you will obtain the amount of oil used for the changes:

`4qt*22oil\text{ }changes=88qt`

He spent 88 quarts of oil for the 22 oil changes.

Finally, to determine how much oil is left in the container, you have to calculate the difference between the initial amount of oil and the oil used in the oil changes:

`160qt-88qt=72qt`

There are 72 quarts of oil left in the container.