Sean and Zara has some money each. If Zara gives Sean $16, he will have 3 times as much money as her. If Sean gives Zara $13, he will have the same amount of money as her. How much money does each person have respectively?
- Sean?
- Zara?
| |
Case 1 |
Case 2 |
| |
Sean |
Zara |
Sean |
Zara |
| Before |
3 u - 16 |
1 u + 16 |
2 u + 13 |
2 u - 13 |
| Change |
+ 16 |
- 16 |
- 13 |
+ 13 |
| After |
3 u |
1 u |
2 u |
2 u |
(a)
If Zara gives Sean some money or Sean gives Zara some money, the total amount of money remains the same.
Total amount that Sean and Zara have in the end for both cases
= 3 u + 1 u
= 4 u
Amount that Sean and Zara each has in the end in Case 2
= 4 u ÷ 2
= 2 u
The amount that Sean has at first in Case 1 and Case 2 is the same.
3 u - 16 = 2 u + 13
3 u - 2 u = 13 + 16
1 u = 29
Amount that Sean has
= 2 u + 13
= 2 x 29 + 13
= 58 + 13
= $71
(b)
Amount that Zara has
= 1 u + 16
= 29 + 16
= $45
Answer(s): (a) $71; (b) $45
