# Eric's gas tank is 16 full. After he buys 11 gallons of gas, it is 23 full. How many gallons can...

## Question:

Eric's gas tank is 16 full. After he buys 11 gallons of gas, it is 23 full. How many gallons can Eric's tank hold?

## Ratios and Proportions:

A ratio is a quantitative comparison between two numbers or quantities by the use of divisions. For example, the speed in meters per second compares the distance covered and the time in minutes. A proportion is a relationship showing the equality between two ratios.

Eric's tank is {eq}\dfrac{1}{6} {/eq} full. This means that when the tank is full to its capacity, then it should be {eq}\dfrac{6}{6} {/eq} full.

When Eric buys 11 gallons of gas, the tank becomes {eq}\dfrac{2}{3} {/eq} full. Thus, the fraction representing the 11 gallons is:

• {eq}\dfrac{2}{3} - \dfrac{1}{6} = \dfrac{1}{2} {/eq}

If {eq}\dfrac{1}{2} {/eq} corresponds to 11 gallons, then what about {eq}\dfrac{6}{6} {/eq}?

• {eq}\dfrac{\dfrac{6}{6}\times 11}{\dfrac{1}{2}} = \boxed{22} {/eq} gallons.

Eric's tank can hold 22 gallons.