Jeremy and Kathy has some money each. If Kathy gives Jeremy $20, he will have 5 times as much money as her. If Jeremy gives Kathy $19, he will have the same amount of money as her. How much money does each person have respectively?
- Jeremy?
- Kathy?
| |
Case 1 |
Case 2 |
| |
Jeremy |
Kathy |
Jeremy |
Kathy |
| Before |
5 u - 20 |
1 u + 20 |
3 u + 19 |
3 u - 19 |
| Change |
+ 20 |
- 20 |
- 19 |
+ 19 |
| After |
5 u |
1 u |
3 u |
3 u |
(a)
If Kathy gives Jeremy some money or Jeremy gives Kathy some money, the total amount of money remains the same.
Total amount that Jeremy and Kathy have in the end for both cases
= 5 u + 1 u
= 6 u
Amount that Jeremy and Kathy each has in the end in Case 2
= 6 u ÷ 2
= 3 u
The amount that Jeremy has at first in Case 1 and Case 2 is the same.
5 u - 20 = 3 u + 19
5 u - 3 u = 19 + 20
1 u = 39
Amount that Jeremy has
= 3 u + 19
= 3 x 39 + 19
= 117 + 19
= $136
(b)
Amount that Kathy has
= 1 u + 20
= 39 + 20
= $59
Answer(s): (a) $136; (b) $59
