SOLUTION: two numbers are in the ratio 3 to 5 if 9 is added to their sum the result is 41 find the numbers

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Question 675676: two numbers are in the ratio 3 to 5 if 9 is added to their sum the result is 41 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
given:
two numbers are in the ratio 3 to 5
so, we have x%2Fy=3%2F5......eq. 1

if 9 is added to their sum the result is 41+

x%2By%2B9=41......eq. 2

solve this system:
so, we have x%2Fy=3%2F5......eq. 1
x%2By%2B9=41......eq. 2
______________________________
x%2Fy=3%2F5......solve for x
x=%283%2F5%29y......substitute in eq. 2
%283%2F5%29y%2By%2B9=41......eq. 2......solve for y
%283%2F5%29y%2By=41-9
%283y%2F5%29%2By=32...both sides multiply by 5
5%283y%2F5%29%2B5y=32%2A5
3y%2B5y=160
8y=160
y=160%2F8
highlight%28y=20%29

now find x

x=%283%2F5%29y
x=%283%2F5%2920
x=%283%2Fcross%285%29%29cross%2820%294
x=3%2A4
highlight%28x=12%29