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Question

The difference between two numbers is $$4$$. If the sum of five times the smaller number and bigger number is $$58$$, find the numbers.


Solution

Let $$x$$ and $$y$$ be the two numbers such that $$x > y$$.
$$x - y = 4 ..... \left( 1 \right)$$

Also,
$$5y + x = 58 ..... \left( 2 \right)$$

Subtracting equation $$\left( 1 \right)$$ from $$\left( 2 \right)$$, we have
$$\left( 5y + x \right) - \left( x - y \right) = 58 - 4\\$$
$$6y = 54$$

$$\Rightarrow y = \cfrac{54}{6} = 9$$

$$\therefore x - 9 = 4 \Rightarrow x = 9 + 4 = 13$$

Hence the two numbers are $$9$$ and $$13$$.

Mathematics

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