# Problem of the Week Problem B and Solution Running Low on Gas

## Problem

Driving home from a meeting late one evening, Ming notices that her gas gauge is showing that a mere $$\frac{1}{10}$$ of a tank remains. Luckily, just then she spots a $$24$$-hour gas station. She has just enough money to add $$20$$ litres of gas to the tank, bringing her gas tank up to $$\frac{1}{2}$$ full.

1. Given that the gas tank went from $$\frac{1}{10}$$ full to $$\frac{1}{2}$$ full, determine the fraction of the tank filled by the gas that Ming added. Hint: Use equivalent fractions.

2. The fraction of the tank you found in part (a) holds $$20$$ L. How many litres are there in $$\frac{1}{10}$$ of a full tank?

3. Given what you discovered in part (b), what is the full capacity, in litres, of Ming’s gas tank?

## Solution

Driving home from a meeting late one evening, Ming notices that her gas gauge is showing that a mere $$\frac{1}{10}$$ of a tank remains. Luckily, just then she spots a $$24$$-hour gas station. She has just enough money to add $$20$$ litres of gas to the tank, bringing her gas tank up to $$\frac{1}{2}$$ full.

1. Given that the gas tank went from $$\frac{1}{10}$$ full to $$\frac{1}{2}$$ full, determine the fraction of the tank filled by the gas that Ming added. Hint: Use equivalent fractions.

2. The fraction of the tank you found in part (a) holds $$20$$ L. How many litres is there in $$\frac{1}{10}$$ of a full tank?

3. Given what you discovered in part (b), what is the full capacity, in litres, of Ming’s gas tank?

Solution

1. Since $$\frac{1}{2}= \frac{5}{10}$$ and Ming started with $$\frac{1}{10}$$ of a tank, the gas Ming added filled $\frac{5}{10}\text{ of a tank}-\frac{1}{10}\text{ of a tank} = \frac{4}{10}\text{ of a tank.}$

2. Since $$\frac{4}{10}$$ of a tank holds 20 litres, $$\frac{1}{10}$$ of a tank holds $$20\div 4=5$$ litres.

3. Since $$\frac{1}{10}$$ of a tank holds $$5$$ litres, the full capacity of Ming’s tank is $$10\times 5 = 50$$ litres.