Answer this word problem...

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?

 

a. 18 gallons
b. 16 gallons
c. 20 gallons
d. 14 gallons

Answer 1

Here's another solution.

$72.96-$42.56=$30.40 extra for 10 gallons of gas

$30.40/10=$3.04 per gallon is being paid

$72.96/$3.04=24 gallons

24 gallons-10 gallons=14 gallons was the original tank which is d)

Answer 2

This is a proportion problem.

 

You may express proportions as ratios (fractions) in multiple ways.  Let's choose to let X be the tank size now.

 

The current size of the tank compared to the cost to fill the current tank is equal to the expanded size of the tank compared to the cost to fill the expanded tank.  Or in math terms,

 

               X / $42.56 = (X+10)/$72.96

                      72.96X = 42.56X + 425.6                    (cross multiply)

                     30.4X = 425.6                               (subtract 42.56X from both sides)

                           X = 14 gal                                 (divide both sides by 30.4)

 

Answer 3

Let's assume that the cost of gas has not changed in the time that Mrs. Hwang expanded her gas tank. Let's say it is $x per gallon.

 

let's assume that the gas tank size is y gallons (before expanding). 

 

Since she pays 42.56 to fill her tank, 

 

y gallons * $x per gallon = 42.56 => x*y = 42.56  , or  x = 42.56/y ...... remember this 

 

With her new tank, she now has (y+10) gallons to fill. Therefore

 

(y+10) gallons * $x per gallon = 72.96 => (y+10) * 42.56/y = 72.96

 

multiplying both sides of the equation by y, we get

 

(y+10) * 42.56 = 72.96y

 

=> 42.56y + 425.6 = 72.96.y , or 30.4y = 425.6, which implies

 

y = 14 gallons 

 

So the original tank was 14 gallons, and the size of her tank after expanding is 14 + 10 = 24 gallons. 

 

Bonus - x = 42.56/y = 42.56/14 = $3.04 . In other words, Mrs. Hwang is paying $3.04 per gallon for gas. 

 

 The answer to the above question is therefore d. 14 gallons