# 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?

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?
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June Rowland
Let the larger number be x and smaller number be y.
$\therefore$ As per the question we get :
$5y-5=x$ and $x+y=61$
Substituting the value of x, that is 5y -5 from the first equation to the second equation - $x+y=61$, we get :
$5y-5+y=61$
$6y-5=61$
$6y=61+5$
$6y=66$
$y=\frac{66}{6}$
$\therefore y=11$
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 .