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