Bobby and Zara has some money each. If Zara gives Bobby $20, he will have 5 times as much money as her. If Bobby gives Zara $10, he will have the same amount of money as her. How much money does each person have respectively?
- Bobby?
- Zara?
| |
Case 1 |
Case 2 |
| |
Bobby |
Zara |
Bobby |
Zara |
| Before |
5 u - 20 |
1 u + 20 |
3 u + 10 |
3 u - 10 |
| Change |
+ 20 |
- 20 |
- 10 |
+ 10 |
| After |
5 u |
1 u |
3 u |
3 u |
(a)
If Zara gives Bobby some money or Bobby gives Zara some money, the total amount of money remains the same.
Total amount that Bobby and Zara have in the end for both cases
= 5 u + 1 u
= 6 u
Amount that Bobby and Zara each has in the end in Case 2
= 6 u ÷ 2
= 3 u
The amount that Bobby has at first in Case 1 and Case 2 is the same.
5 u - 20 = 3 u + 10
5 u - 3 u = 10 + 20
1 u = 30
Amount that Bobby has
= 3 u + 10
= 3 x 30 + 10
= 90 + 10
= $100
(b)
Amount that Zara has
= 1 u + 20
= 30 + 20
= $50
Answer(s): (a) $100; (b) $50
