SOLUTION: i need help with this problem divide 56 into two parts such that 3/8 of the larger number decreased by 6 equals 1/4 of the smaller number.

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Question 442927: i need help with this problem
divide 56 into two parts such that 3/8 of the larger number decreased by 6 equals 1/4 of the smaller number.
Answer by swincher4391(1107) About Me  (Show Source):
You can put this solution on YOUR website!
So let's let the two parts be x and y. Let x be the larger number.
Then x%2By+=+56 and expr%283%2F8%29x-6+=+expr%281%2F4%29y
You have yourself a system of equations. Two unknowns, two equations. It's solvable.
x+y = 56 ---> x = 56 -y
Then
expr%283%2F8%29%2A%2856-y%29+-6+=+expr%281%2F4%29y
21+-+expr%283%2F8%29y+-6+=+expr%281%2F4%29y
15+-+expr%283%2F8%29y+=+expr%281%2F4%29y
Let's multiply everything by 8.
120-+3y+=+2y
120+=+5y
y+=+24
x+%2B+24+=+56 based on our first equation.
x+=+56-24+=+32
So our numbers are 32 and 24.