George and Japheth were given some allowances each. If George spent $10 each day and Japheth spent $20 each day, George would still have $972 left when Japheth spent all his allowance. If George spent $20 each day and Japheth spent $10 each day, George would still have $42 left when Japheth spent all his allowance.
- How much allowance did George receive?
- How much allowance did Japheth receive?
|
Case 1 |
Case 2 |
|
George |
Japheth |
George |
Japheth |
Before |
1 u + 972 |
2 u |
2 p + 42 |
1 p |
Change |
- 1 u |
- 2 u |
- 2 p |
- 1 p |
After |
972 |
0 |
42 |
0 |
(a)
Simplify the ratio.
10 : 20 = 1 : 2
The allowance that Japheth had at first is the same for Case 1 and Case 2.
1 p = 2 u
2 p = 4 u
The allowance that George had at first is the same for Case 1 and Case 2.
4 u + 42 = 1 u + 972
4 u - 1 u = 972 - 42
3 u = 930
1 u = 930 ÷ 3 = 310
Allowance that George received
= 1 u + 972
= 310 + 972
= $1282
(b)
Allowance that Japheth received
= 2 u
= 2 x 310
= $620
Answers: (a) $1282; (b) $620