SOLUTION: 1.The income of A and B are in the ratio 4:3 and their expenditure are in ratio 3:2 . If they both save 6oo cedis at the end of th year, find the annual income of each.

Question 1095518: 1.The income of A and B are in the ratio 4:3 and their expenditure are in ratio 3:2 . If they both save 6oo cedis at the end of th year, find the annual income of each.
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!

let Ai equal the income of A.
let Ae equal the expense of A.

let Bi equal the income of B.
let Be equal the expense of B.

the ratio of A income to B income is equal to 4/3.
therefore Ai/Bi = 4/3
from this you can determine that Ai = 4/3 * Bi

the ratio of A expense to B expense is equal to 3/2.
therefore Ae/Be = 3/2
from this you can determine that Ae = 3/2 * Be

each of them saves 600 cedis.

since what they save is equal to their income minus their expenses, you get:

Ai - Ae = 600
Bi = Be = 600

since Ai = 4/3 * Bi and Ae = 3/2 * Be, you can replace Ai and Ae with their equivalents to get:

4/3 * Bi - 3/2 * Be = 600
Bi - Be = 600

these are two equations that need to be solved simultaneously.

i will solve by elimination.

multiply both sides of the first equation by 2/3 and leave the second equation as is to get:

8/9 * Bi - Be = 400
Bi - Be = 600

since Bi is equal to 9/9 * Bi, these equations become:

8/9 * Bi - Be = 400
9/9 * Bi - Be = 600

subtract the first equation from the second and you get:

1/9 * Bi = 200

solve for Bi to get Bi = 9 * 200 = 1800

since Ai = 4/3 * Bi, then Ai = 2400

you started with:

Ai - Ae = 600

since Ai = 2400, then solve for Ae to get Ae = 2400 - 600 = 1800.

you started with:

Bi - Be = 600

since Bi = 1800, then solve for Be to get Be = 1800 - 600 = 1200

your solutions are:

Ai = 2400
Ae = 1800

Bi = 1800
Be = 1200

the ratio of Ai to Bi is 2400 / 1800 = 4/3

the ratio of Ae to Be is 1800 / 1200 = 3/2

Ai - Ae becomes 2400 - 1800 = 600
Bi - Be becomes 1800 - 1200 = 600

600 is the annual saving of each.

everything checks out.

you are asked to find the annual income of each.

your solution is that the annual income of A is 2400 cedis and the annual income of B is 1800 cedis.

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