SOLUTION: If one-half the smaller of number is increased by one-third the larger number, the result os 2. If one-third the snakker number increased by one-ninth the larger number, the result

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Question 335905: If one-half the smaller of number is increased by one-third the larger number, the result os 2. If one-third the snakker number increased by one-ninth the larger number, the result is 1. Find the numbers.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Let x = the smaller number
Let y = the larger number
:
Write an equation for each statement:
"If one-half the smaller of number is increased by one-third the larger number, the result is 2."
1%2F2x + 1%2F3y = 2
:
"If one-third the smaller number increased by one-ninth the larger number, the result is 1."
1%2F3x + 1%2F9y = 1
:
Multiply the 1st equation by 6, multiply the 2nd equation by 18
Subtract the 1st resulting equation from the 2nd resulting equation
6x + 2y = 18
3x + 2y = 12
----------------subtracting eliminates y, find x
3x = 6
x = 2
:
Find y using the equation 6x + 2y = 18
6(2) + 2y = 18
2y = 18 - 12
2y = 6
y = 3
:
:
Check solutions in the 1st original equation
1%2F2(2) + 1%2F3(3) = 2
2%2F2 + 3%2F3 = 2; confirms our solutions