Ben and Liam were given some allowances each. If Ben spent $14 each day and Liam spent $28 each day, Ben would still have $1020 left when Liam spent all his allowance. If Ben spent $28 each day and Liam spent $14 each day, Ben would still have $96 left when Liam spent all his allowance.
- How much allowance did Ben receive?
- How much allowance did Liam receive?
|
Case 1 |
Case 2 |
|
Ben |
Liam |
Ben |
Liam |
Before |
1 u + 1020 |
2 u |
2 p + 96 |
1 p |
Change |
- 1 u |
- 2 u |
- 2 p |
- 1 p |
After |
1020 |
0 |
96 |
0 |
(a)
Simplify the ratio.
14 : 28 = 1 : 2
The allowance that Liam had at first is the same for Case 1 and Case 2.
1 p = 2 u
2 p = 4 u
The allowance that Ben had at first is the same for Case 1 and Case 2.
4 u + 96 = 1 u + 1020
4 u - 1 u = 1020 - 96
3 u = 924
1 u = 924 ÷ 3 = 308
Allowance that Ben received
= 1 u + 1020
= 308 + 1020
= $1328
(b)
Allowance that Liam received
= 2 u
= 2 x 308
= $616
Answers: (a) $1328; (b) $616