Japheth and Rachel has some money each. If Rachel gives Japheth $20, he will have 3 times as much money as her. If Japheth gives Rachel $17, he will have the same amount of money as her. How much money does each person have respectively?
- Japheth?
- Rachel?
| |
Case 1 |
Case 2 |
| |
Japheth |
Rachel |
Japheth |
Rachel |
| Before |
3 u - 20 |
1 u + 20 |
2 u + 17 |
2 u - 17 |
| Change |
+ 20 |
- 20 |
- 17 |
+ 17 |
| After |
3 u |
1 u |
2 u |
2 u |
(a)
If Rachel gives Japheth some money or Japheth gives Rachel some money, the total amount of money remains the same.
Total amount that Japheth and Rachel have in the end for both cases
= 3 u + 1 u
= 4 u
Amount that Japheth and Rachel each has in the end in Case 2
= 4 u ÷ 2
= 2 u
The amount that Japheth has at first in Case 1 and Case 2 is the same.
3 u - 20 = 2 u + 17
3 u - 2 u = 17 + 20
1 u = 37
Amount that Japheth has
= 2 u + 17
= 2 x 37 + 17
= 74 + 17
= $91
(b)
Amount that Rachel has
= 1 u + 20
= 37 + 20
= $57
Answer(s): (a) $91; (b) $57
