Question

The sum of $127 was divided among 3 people so that the second received $5 less than twice as much as the first and third received $2 more than the second how much did each receive

Answer 1

let the 1st received be x

let the 2nd received be 2x-5

let the 3rd received be 2x-5t+2= 2x+3

Total=127

x+2x-5+2x-3=127

5x=135.

x=27 is for the 1st person

2x-5=2×27-5=49 is for the 2nd person

2x-5=2×27-3=51.

Answer 2

1. $27
2. $49
3. $51

Explanation:

The given relations let us write three equations in the unknown quantities.

Setup

Let x, y, z represent the amounts received by the first, second, and third person, respectively. Then the problem statement tells us ...

x + y + z = 127 . . . . . . $127 was divided

2x - y = 5 . . . . . . . . second got $5 less than twice the first

-y +z = 2 . . . . . . . third got $2 more than the second

Solution

Subtracting the second equation from twice the first gives ...

2(x +y +z) -(2x -y) = 2(127) -(5)

3y +2z = 249 . . . . . . . simplify (x is eliminated)

Subtracting twice the third equation gives ...

(3y +2z) -2(-y +z) = (249) -2(2)

5y = 245 . . . . . . . . simplify (z is eliminated)

y = 49 . . . . . . . . . divide by 5

z = 2+y = 51 . . . . find z

x = 127 -(49 +51) = 27 . . . . find x

The first received $27; the second received $49; and the third received $51.