Question

The gas tank in Yadira's car was 3/8 of the way full in the morning: After she commuted to work; the gas tank was only of 1/4 the way full. If Yadira's car used 1 1/2 gallons of gas during her commute to work, how many gallons of gas does her car's gas tank hold when it is completely full? Show your work:

Answer 1

Given that:

- The following fraction represents how full the gas tank in Yadira's car was in the morning:

`(3)/(8)`

- This fraction represents how full the gas tank in Yadira's car was after she commuted to work:

`(1)/(4)`

- This Mixed Number represents the number of gallons of gas her car used during her commute to work:

`1(1)/(2)`

You can convert the Mixed Number to an Improper Fraction by multiplying the whole number part by the denominator of the fraction and then adding the result to the numerator. The denominator does not change:

`1(1)/(2)=((1\cdot2)+1)/(2)=(2+1)/(2)=(3)/(2)`

Then, let be "x" the number of gallons of gas Yadira's car gas tank holds when it is completely full.

You can set up the following equation:

`(3)/(8)x-(3)/(2)=(1)/(4)x`

Now you need to solve for "x":

`(3)/(8)x-(1)/(4)x=(3)/(2)`
`(1)/(8)x=(3)/(2)`
`x=(3)/(2)\cdot8`
`\begin{gathered} x=(3\cdot8)/(2) \\ \\ x=(24)/(2) \\ \\ x=12 \end{gathered}`

Hence, the answer is:

`12\text{ }gallons`