SOLUTION: The sum of N1200 is invested in three project X,Y,Z at the ratio of 4,5,6 respectively. The expected cash inflow per annum is N700. the combined income for projects X and Y is N140

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Question 1022451: The sum of N1200 is invested in three project X,Y,Z at the ratio of 4,5,6 respectively. The expected cash inflow per annum is N700. the combined income for projects X and Y is N140 more than the income from project Z. What is the combined cash inflow for projects x and y.
Answer by Theo(13342) About Me  (Show Source):
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investments:

the amount invested in projects x and y and z is equal to 1200.

ratio of the amount invested in projects x and y and z is 4 to 5 to 6.

if we let a be the common factor, then we get:

4a is the amount invested in x.
5a is the amount invested in y.
6a is the amount invested in z.

therefore we get:

4a + 5a + 6a = 1200

combine like terms to get 15a = 1200.

solve for a to get a = 80.

the value of the common factor of a is 80.

the amount invested in project x is 4 * 80 = 320.
the amount invested in project y is 5 * 80 = 400.
the amount invested in project z is 6 * 80 = 480.

add them up and you get a total investment of 1200.

income:

total income is 700 per year.

let b represent the income for project x.
let c represent the income for project y.
let d represent the income for project z.

total income is equal to 700.

therefore:

b + c + d = 700.

combined income for project x and y is equal to 140 more than the incomes for project z.

therefore:

b + c = d + 140.

since b + c = d + 140, then the equation of b + c + d = 700 becomes d + 140 + d = 700, after you replace b + c with d + 140.

the equation has becomes d + 140 + d = 700.

combine like terms to get 2d + 140 = 700.

subtract 140 from both sides to get 2d = 560.

divide both sides by 2 to get d = 280.

since d = 280, then b + c = d + 140 becomes b + c = 280 + 140 which becomes b + c = 420.

b + c + d therefore becomes 420 + 280 = 700.

numbers check out, so your solution is:

the combined cash flow incoming for projects x and y is equal to b + c which is equal to 420.