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?

Question

Abigail Allen · Accepted Answer

The two numbers are 50 and 11.

Let the larger number be #x# and smaller number be #y#. #:.# As per the question we get : #5y - 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 : #5y - 5 + y = 61# #6y - 5 = 61# #6y = 61 + 5# #6y = 66# #y = 66/6# #:. y = 11# Now substituting this value in the equation #x + y = 61#, we get : #x + 11 = 61# #:. x = 61 - 11 = 50# Hence the two numbers are 50 and 11 .

Savannah Anderson · Answer

undefined Let's denote the larger number as $ x $ and the smaller number as $ y $.

Given:
1. The larger number is 5 less than 5 times the smaller number: $ x = 5y - 5 $
2. The sum of the two numbers is 61: $ x + y = 61 $

Now, we can solve this system of equations.

From equation (1), we can express $ x $ in terms of $ y $: $ x = 5y - 5 $

Substitute this expression for $ x $ into equation (2):

$$ 5y - 5 + y = 61 $$

Combine like terms:

$$ 6y - 5 = 61 $$

Add 5 to both sides:

$$ 6y = 66 $$

Divide both sides by 6:

$$ y = 11 $$

Now that we have found the value of $ y $, we can substitute it back into equation (1) to find the value of $ x $:

$$ x = 5(11) - 5 $$
$$ x = 55 - 5 $$
$$ x = 50 $$

So, the smaller number is 11 and the larger number is 50.