The Sum Of Two Numbers Is 78. If The Smaller Number Is Added By 10 And The Larger Is Subtracted By 8, Their Ratio Will Be 1:1. What Are The Numbers.

The sum of two numbers is 78. If the smaller number is added by 10 and the larger is subtracted by 8, their ratio will be 1:1. What are the numbers.

  Let x be the smaller number
let y be the larger number
x + y = 78 --equation1
x + 10 = y - 8 ----equation2
from equation 1
x + y = 78
y = 78-x --equation 1
Substitute equation 1 to equation 2
x + 10 = (78 - x) - 8
x + 10 = 78 - x - 8
Transpose
x + x = 78 - 8 - 10
2x = 60
x = 60/2
x = 30
Substitute x = 30 to equation 1
y = 78-x
y =78-30
y = 48
Therefore the numbers are 30 and 48