Question

guided practice
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?

	size of tank (gal)	price per gallon	cost to fill
new tank	( g + 10 )	( p )	72.96

type your answer and then click or tap done.
solve ( \frac{42.56}{g} = \frac{72.96}{g + 10} ).
( g = ) blank

Explanation:

Step1: Cross - multiply the equation

Given the equation \(\frac{42.56}{g}=\frac{72.96}{g + 10}\), cross - multiplying (if \(\frac{a}{b}=\frac{c}{d}\), then \(a\times d=b\times c\)) gives us \(42.56\times(g + 10)=72.96\times g\).

Step2: Expand the left - hand side

Using the distributive property \(a\times(b + c)=a\times b+a\times c\), we have \(42.56g+42.56\times10 = 72.96g\).
Calculating \(42.56\times10 = 425.6\), so the equation becomes \(42.56g + 425.6=72.96g\).

Step3: Move the terms with \(g\) to one side

Subtract \(42.56g\) from both sides of the equation: \(425.6=72.96g - 42.56g\).

Step4: Combine like terms

\(72.96g-42.56g=(72.96 - 42.56)g = 30.4g\), so the equation is \(425.6 = 30.4g\).

Step5: Solve for \(g\)

Divide both sides of the equation by \(30.4\): \(g=\frac{425.6}{30.4}\).
Calculating \(\frac{425.6}{30.4}=14\).

Answer:

The size of the old tank is \(14\) gallons, and the size of the new tank (which is what the question asks for "how large is her tank now") is \(g + 10=14 + 10 = 24\) gallons. But if we consider the value of \(g\) (old tank) first, \(g = 14\). However, since the question is "how large is her tank now" (new tank), the answer is \(24\) gallons. If we consider the old tank, the answer is \(14\) gallons. But from the equation \(\frac{42.56}{g}=\frac{72.96}{g + 10}\), solving for \(g\) (old tank) gives \(g = 14\), and the new tank (now) is \(g+10 = 24\) gallons.