The sum of two numbers is 80 . The larger number exceeds four times the smaller one by 5 . Find the numbers.

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The sum of two numbers is 80 . The larger number exceeds four times the smaller one by 5 . Find the numbers.

Solution:

Suppose the larger number be $\mathrm{x}$ and the smaller number be $\mathrm{y}$ .
Then according to the question
$\begin{array}{l} x+y=80\dots \dots(i) \\ x=4 y+5 \\ x-4 y=5\dots \dots(ii) \end{array}$
Subtracting equation(ii) from equation(i), we obtain
$5 \mathrm{y}=75 \Rightarrow \mathrm{y}=15$
Now, putting $\mathrm{y}=15 \mathrm{in}$ equation(i), we get
$x+15=80 \Rightarrow x=65$
As a result, the numbers are 65 and 15