Competition problem — Algebra — Maths Olympiad Prep

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Algebra Difficulty 3.9 AMC 10/12 Find the answer South Africa

When a water-tank is $30\%$ empty it has $30$ litres more in it than when it is $30\%$ full. How many litres can the tank hold when it is full?

Your answer

A number or a short expression. Spacing and $ signs are ignored.

Solution

$75$

If $W$ is the number of litres the tank can hold, then when it is $30\%$ empty it is holding $0.7W$ litres, and so we have $0.7W = 0.3W + 30$ , i.e. $0.4W = 30$ and then $W = 30 \div 0.4 = 300 \div 4 = 75$ .

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