Dylan and Sarah has some money each. If Sarah gives Dylan $20, he will have 7 times as much money as her. If Dylan gives Sarah $17, he will have the same amount of money as her. How much money does each person have respectively?
- Dylan?
- Sarah?
| |
Case 1 |
Case 2 |
| |
Dylan |
Sarah |
Dylan |
Sarah |
| Before |
7 u - 20 |
1 u + 20 |
4 u + 17 |
4 u - 17 |
| Change |
+ 20 |
- 20 |
- 17 |
+ 17 |
| After |
7 u |
1 u |
4 u |
4 u |
(a)
If Sarah gives Dylan some money or Dylan gives Sarah some money, the total amount of money remains the same.
Total amount that Dylan and Sarah have in the end for both cases
= 7 u + 1 u
= 8 u
Amount that Dylan and Sarah each has in the end in Case 2
= 8 u ÷ 2
= 4 u
The amount that Dylan has at first in Case 1 and Case 2 is the same.
7 u - 20 = 4 u + 17
7 u - 4 u = 17 + 20
1 u = 37
Amount that Dylan has
= 4 u + 17
= 4 x 37 + 17
= 148 + 17
= $165
(b)
Amount that Sarah has
= 1 u + 20
= 37 + 20
= $57
Answer(s): (a) $165; (b) $57
