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?

2k1ablakrh0
2022-09-23
Answered

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June Rowland

Answered 2022-09-24
Author has **6** answers

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 .

$\therefore$ 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 .

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