SOLUTION: Dear beloved tutors, Two numbers is differ by 8. If one-half the large is added to one-fourth the smaller, the resulting some is 22. Find the numbers.

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Question 1020887: Dear beloved tutors, Two numbers is differ by 8. If one-half the large is added to one-fourth the smaller, the resulting some is 22. Find the numbers.
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

let numbers be x and y
if numbers is differ by 8, we have
x-y=8...........eq.1 (assuming x is greater number)
if one-half the large, which is %281%2F2%29x is added to one-fourth the smaller, which is %281%2F4%29y, the resulting some is 22, we have
%281%2F2%29x+%2B%281%2F4%29y=22........eq.2
go to x-y=8...........eq.1 and solve for x
x=8%2By...substitute in eq.2
%281%2F2%29%288%2By%29+%2B%281%2F4%29y=22........eq.2 and solve for y
%281%2F2%29%288%2By%29+%2B%281%2F4%29y=22.....both sides multiply by 4
4%281%2F2%29%288%2By%29+%2B4%281%2F4%29y=4%2A22
2%288%2By%29+%2By=88
16%2B2y+%2By=88
3y=88-16
3y=72
y=72%2F3
highlight%28y=24%29
now find x
x=8%2By
x=8%2B24
highlight%28x=32%29

so, your numbers are: highlight%2824%29 and highlight%2832%29