# The larger of 2 numbers is 5 less than 5 times the smaller number. The sum of the two numbers is 61. What are the two numbers?

May 5, 2018

The two numbers are 50 and 11.

#### Explanation:

Let the larger number be $x$ and smaller number be $y$.

$\therefore$ As per the question we get :

$5 y - 5 = x$ and $x + y = 61$

Substituting the value of $x$, that is 5$y$ -5 from the first equation to the second equation - $x + y = 61$, we get :

$5 y - 5 + y = 61$

$6 y - 5 = 61$

$6 y = 61 + 5$

$6 y = 66$

$y = \frac{66}{6}$

$\therefore y = 11$

Now substituting this value in the equation $x + y = 61$, we get :

$x + 11 = 61$

$\therefore x = 61 - 11 = 50$

Hence the two numbers are 50 and 11 .