Question 1095518


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.