SOLUTION: If two numbers total 107 5/6 and if three times the smaller number is 13 5/6 less than the larger number, what is the larger number?

Question 1035233: If two numbers total 107 5/6 and if three times the smaller number is 13 5/6 less than the larger number, what is the larger number?
Answer by Cromlix(4381) (Show Source): You can put this solution on YOUR website!
Hi there,
two numbers total 107 5/6
x + y = 107 5/6
x + y = 647/6.......(1)
three times the smaller number is 13 5/6 less than the larger number.
3x = y - 13 5/6
3x - y = - 83/6.....(2)
...............
x + y = 647/6.......(1)
3x - y = - 83/6.....(2)
Add Eq(1) + (2)
4x = 647/6 + (- 83/6)
4x = 647/6 - 83/6
4x = 564/6
x = 564/24
x = 47/2
Substitute x = 47/2 in
x + y = 647/6.......(1)
47/2 + y = 647/6
y = 647/6 - 47/2
y = (647 - 141)/6
y = 506/6.
y = 253/3
So x = 23 1/2
y = 84 1/3. (The larger number)
Proof:
x + y = 647/6
47/2 + 253/3 = (141 + 506)/6 = 647/6.
Hope this helps :-)
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