Daniel and Sarah has some money each. If Sarah gives Daniel $20, he will have 7 times as much money as her. If Daniel gives Sarah $19, he will have the same amount of money as her. How much money does each person have respectively?
- Daniel?
- Sarah?
|
Case 1 |
Case 2 |
|
Daniel |
Sarah |
Daniel |
Sarah |
Before |
7 u - 20 |
1 u + 20 |
4 u + 19 |
4 u - 19 |
Change |
+ 20 |
- 20 |
- 19 |
+ 19 |
After |
7 u |
1 u |
4 u |
4 u |
(a)
If Sarah gives Daniel some money or Daniel gives Sarah some money, the total amount of money remains the same.
Total amount that Daniel and Sarah have in the end for both cases
= 7 u + 1 u
= 8 u
Amount that Daniel and Sarah each has in the end in Case 2
= 8 u ÷ 2
= 4 u
The amount that Daniel has at first in Case 1 and Case 2 is the same.
7 u - 20 = 4 u + 19
7 u - 4 u = 19 + 20
1 u = 39
Amount that Daniel has
= 4 u + 19
= 4 x 39 + 19
= 156 + 19
= $175
(b)
Amount that Sarah has
= 1 u + 20
= 39 + 20
= $59
Answer(s): (a) $175; (b) $59