Answer:
- $27
- $49
- $51
Step-by-step 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.
