SOLUTION: Four times the larger of 2 numbers exceeds their sum by 25; four times the smaller number exceeds their difference by 1. What are the numbers?

Question 523043: Four times the larger of 2 numbers exceeds their sum by 25; four times the smaller number exceeds their difference by 1. What are the numbers?
Answer by Maths68(1474) (Show Source): You can put this solution on YOUR website!
Let
Larger Number = x
Smaller Number = y
4*(larger number)=(Sum of Numbers)+25
4x=x+y+25
4x-x-y=25
3x-y=25...............(1)
4*(Smaller number)=(Difference of numbers)+1
4y=x-y+1
4y+y-x=1
5y-x=1................(2)
Multiply (2) by 3 and add to (1)
3x-y=25
15y-3x=3
------------
14y=28
14y/14=28/14
y=2
Put the value of y in (1)
3x-y=25
3x-2=25
3x=25+2
3x=27
3x/3=27/3
x=9

Larger Number = x = 9
Smaller Number = y = 2

Check
=====
Sum of Numbers = x+y = 9+2 = 11
4*(larger number)=(Sum of Numbers)+25
4*9 = 11+25
36=36
Difference of Numbers = x-y=9-2=7
4*(Smaller number)=(Difference of numbers)+1
4*2=7 + 1
8=8

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