Question

The sum of $224 was divided among 3 people so that the second person received $1 less than twice as much as the first, and the third received $11 more than second. How much did each person receive? 1st person: 2nd person: 3rd person: show work

Answer 1

• 1st person: $43
• 2nd person: $85
• 3rd person: $96

Explanation:

Let a, b, c represent the amounts received by the first, second, and third person, respectively.

2a-1 = b

c = b+11

a + b + c = 224

Substituting for c, we have ...

a + b + b+11 = 224

a +2b = 213

Substituting for b, we have ...

a +2(2a -1) = 213

a +4a -2 = 213 . . . . . eliminate parentheses

5a = 215 . . . . . . . . . . add 2

a = 43 . . . . . . . . . . . . .divide by 5

b = 2a -1 = 2(43) -1 = 85

c = b +11 = 85 +11 = 96

The amounts received were ...

• 1st person: $43
• 2nd person: $85
• 3rd person: $96