Pierre and Bobby were given some allowances each. If Pierre spent $14 each day and Bobby spent $28 each day, Pierre would still have $605 left when Bobby spent all his allowance. If Pierre spent $28 each day and Bobby spent $14 each day, Pierre would still have $59 left when Bobby spent all his allowance.
- How much allowance did Pierre receive?
- How much allowance did Bobby receive?
|
Case 1 |
Case 2 |
|
Pierre |
Bobby |
Pierre |
Bobby |
Before |
1 u + 605 |
2 u |
2 p + 59 |
1 p |
Change |
- 1 u |
- 2 u |
- 2 p |
- 1 p |
After |
605 |
0 |
59 |
0 |
(a)
Simplify the ratio.
14 : 28 = 1 : 2
The allowance that Bobby had at first is the same for Case 1 and Case 2.
1 p = 2 u
2 p = 4 u
The allowance that Pierre had at first is the same for Case 1 and Case 2.
4 u + 59 = 1 u + 605
4 u - 1 u = 605 - 59
3 u = 546
1 u = 546 ÷ 3 = 182
Allowance that Pierre received
= 1 u + 605
= 182 + 605
= $787
(b)
Allowance that Bobby received
= 2 u
= 2 x 182
= $364
Answers: (a) $787; (b) $364