Sean and Zoe has some money each. If Zoe gives Sean $19, he will have 3 times as much money as her. If Sean gives Zoe $13, he will have the same amount of money as her. How much money does each person have respectively?
- Sean?
- Zoe?
| |
Case 1 |
Case 2 |
| |
Sean |
Zoe |
Sean |
Zoe |
| Before |
3 u - 19 |
1 u + 19 |
2 u + 13 |
2 u - 13 |
| Change |
+ 19 |
- 19 |
- 13 |
+ 13 |
| After |
3 u |
1 u |
2 u |
2 u |
(a)
If Zoe gives Sean some money or Sean gives Zoe some money, the total amount of money remains the same.
Total amount that Sean and Zoe have in the end for both cases
= 3 u + 1 u
= 4 u
Amount that Sean and Zoe 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 - 19 = 2 u + 13
3 u - 2 u = 13 + 19
1 u = 32
Amount that Sean has
= 2 u + 13
= 2 x 32 + 13
= 64 + 13
= $77
(b)
Amount that Zoe has
= 1 u + 19
= 32 + 19
= $51
Answer(s): (a) $77; (b) $51
