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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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