SOLUTION: the sum of two numbers is 61. Five times the smaller number is 23 more than larger. Find the numbers.

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Question 1137321: the sum of two numbers is 61. Five times the smaller number is 23 more than larger. Find the numbers.
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

let's the numbers be x and the smaller number y
if the sum of two numbers is 61 we have
x%2By=61
=>x=61-y....eq.1
if five times the smaller number is 23 more than larger, we have
5y=x%2B23
=>x=5y-23........eq.2
from eq.1 and eq.2 we have
=>5y-23=61-y........solve for y
5y%2By=61%2B23
6y=84
y=84%2F6
y=14
go to x=5y-23........eq.2 plug in y value
x=5%2A14-23
x=47

so, your numbers are:47 and 14