SOLUTION: Divide 15 into two parts such that when the larger is divided by 3 and the smaller is divided by 2 the quotients are equal

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Question 1152980: Divide 15 into two parts such that when the larger is divided by 3 and the smaller is divided by 2 the quotients are equal
Found 2 solutions by MathLover1, MathTherapy:
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

let larger part be x and smaller part y

x%2By=15
x=15-y.........eq.1
when the larger is divided by 3 and the smaller is divided by 2+ the quotients are equal:
x%2F3=y%2F2.......solve for x
x=3y%2F2.......eq.2
from eq.1 and eq.2 we have
15-y=3y%2F2........solve for y
30-2y=3y
30=3y%2B2y
5y=30
y=6
then
x=15-y.........eq.1
x=15-6
x=9
two parts are 9 and 6

Answer by MathTherapy(10551) About Me  (Show Source):
You can put this solution on YOUR website!

Divide 15 into two parts such that when the larger is divided by 3 and the smaller is divided by 2 the quotients are equal 
Now that you've seen the LONG way to do this, let me show you the SHORT and EASY way.

Let the larger be L

Then the smaller is 15 - L

We then get: matrix%281%2C3%2C+L%2F3%2C+%22=%22%2C+%2815+-+L%29%2F2%29

2L = 3(15 - L) ------ Cross-multiplying

2L = 45 - 3L

5L = 45