Question

Mrs. Hwang is taking her vehicle to the shop to have the gas tank expanded by 10 gallons. Now, it costs her $42.56 to fill the tank. Once the new tank is in, it will cost her $72.96. How large is her tank now?

Answer 1

her tank is having capacity of 14 gallons.

Explanation:

Mrs. Hwang is taking her vehicle to the shop to have the gas tank expanded by 10 gallons.

Let initially the capacity of her tank was = x gallons

After expansion it will become = (x + 10) gallons.

Initially cost of filling the x gallons was = $42.56

and after expansion, cost of filling the tank = $72.96

In this process cost of gas remains the same. So we will find per gallon cost of gas before the expansion of tank and after the expansion and equate them to get the value of (x).

`(42.56)/(x)=(72.96)/(x+10)`

By cross multiplication

72.96x = ( x + 10 ) 42.56

72.96x = 42.56x + 425.60 ( By distribution )

72.96x - 42.56x = 425.60

( 30 -4 )x = 425.60

x =
`(425.60)/(30.4) = 14gallons`

Therefore, her tank is having capacity of 14 gallons.

Answer 2

Proportion states that the two fractions or ratios are equal

As per the statement: Mrs. Hwang is taking her vehicle to the shop to have the gas tank expanded by 10 gallons. Now, it costs her $42.56 to fill the tank. Once the new tank is in, it will cost her $72.96

Let the tank size now be x

Since, the gas tank expanded by 10 gallons = x + 10

by definition of proportion ;

`(x)/(42.56)=(x+10)/(72.96)`

by cross multiply we get;

`72.96x = 42.56(x+10)`

using distributive property;
`a\cdot (b+c) =a\cdot b + a\cdot c`

`72.96x = 42.56x+425.6`

Subtract 42.56x from both sides we get;

`30.4x =425.6`

Divide both sides by 30.4 we get;

x = 14

Therefore, the tank is her now is, 14 gallons