Bobby and Archie were given some allowances each. If Bobby spent $11 each day and Archie spent $33 each day, Bobby would still have $1922 left when Archie spent all his allowance. If Bobby spent $33 each day and Archie spent $11 each day, Bobby would still have $74 left when Archie spent all his allowance.
- How much allowance did Bobby receive?
- How much allowance did Archie receive?
|
Case 1 |
Case 2 |
|
Bobby |
Archie |
Bobby |
Archie |
Before |
1 u + 1922 |
3 u |
3 p + 74 |
1 p |
Change |
- 1 u |
- 3 u |
- 3 p |
- 1 p |
After |
1922 |
0 |
74 |
0 |
(a)
Simplify the ratio.
11 : 33 = 1 : 3
The allowance that Archie had at first is the same for Case 1 and Case 2.
1 p = 3 u
3 p = 9 u
The allowance that Bobby had at first is the same for Case 1 and Case 2.
9 u + 74 = 1 u + 1922
9 u - 1 u = 1922 - 74
8 u = 1848
1 u = 1848 ÷ 8 = 231
Allowance that Bobby received
= 1 u + 1922
= 231 + 1922
= $2153
(b)
Allowance that Archie received
= 3 u
= 3 x 231
= $693
Answers: (a) $2153; (b) $693