SOLUTION: The income of A and B are in ratio 3:2 and their expenditures in the ratio 5:3. If each saves #1000, A's income is?

Question 986556: The income of A and B are in ratio 3:2 and their expenditures in the ratio 5:3. If each saves #1000, A's income is?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
The income of A and B are in ratio 3:2 and their expenditures in the ratio 5:3.
If each saves #1000, A's income is?
:
let x = the multiplier for income
then
3x = A's income
2x = B's income
:
let y = the multiplier for expenditures
then
5y = A's expenditure
3y = B's "
:
An equation for each savings
3x - 5y = 1000
2x - 3y = 1000
Use elimination here, multiply the 1st eq by 2, the 2nd by 3
6x - 10y = 2000
6x - 9y = 3000
----------------Subtraction eliminates x, find y
0 - y = -1000
y = 1000 is the expenditure multiplier
Find x using the 1st equation 3x - 5y = 1000
3x - 5(1000) = 1000
3x - 5000 = 1000
3x = 1000 + 5000
3x = 6000
x = 2000 is the income multiplier
therefore
A's income: 3(2000) = $6000
:
:
See if that checks out, find A's expenditures 5(1000) = $5000
6000 - 5000 = $1000
:
You can confirm this with B

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