Ken and Sarah has some money each. If Sarah gives Ken $10, he will have 5 times as much money as her. If Ken gives Sarah $20, he will have the same amount of money as her. How much money does each person have respectively?
- Ken?
- Sarah?
| |
Case 1 |
Case 2 |
| |
Ken |
Sarah |
Ken |
Sarah |
| Before |
5 u - 10 |
1 u + 10 |
3 u + 20 |
3 u - 20 |
| Change |
+ 10 |
- 10 |
- 20 |
+ 20 |
| After |
5 u |
1 u |
3 u |
3 u |
(a)
If Sarah gives Ken some money or Ken gives Sarah some money, the total amount of money remains the same.
Total amount that Ken and Sarah have in the end for both cases
= 5 u + 1 u
= 6 u
Amount that Ken and Sarah each has in the end in Case 2
= 6 u ÷ 2
= 3 u
The amount that Ken has at first in Case 1 and Case 2 is the same.
5 u - 10 = 3 u + 20
5 u - 3 u = 20 + 10
1 u = 30
Amount that Ken has
= 3 u + 20
= 3 x 30 + 20
= 90 + 20
= $110
(b)
Amount that Sarah has
= 1 u + 10
= 30 + 10
= $40
Answer(s): (a) $110; (b) $40
