Albert and Jaslyn has some money each. If Jaslyn gives Albert $15, he will have 3 times as much money as her. If Albert gives Jaslyn $20, he will have the same amount of money as her. How much money does each person have respectively?
- Albert?
- Jaslyn?
| |
Case 1 |
Case 2 |
| |
Albert |
Jaslyn |
Albert |
Jaslyn |
| Before |
3 u - 15 |
1 u + 15 |
2 u + 20 |
2 u - 20 |
| Change |
+ 15 |
- 15 |
- 20 |
+ 20 |
| After |
3 u |
1 u |
2 u |
2 u |
(a)
If Jaslyn gives Albert some money or Albert gives Jaslyn some money, the total amount of money remains the same.
Total amount that Albert and Jaslyn have in the end for both cases
= 3 u + 1 u
= 4 u
Amount that Albert and Jaslyn each has in the end in Case 2
= 4 u ÷ 2
= 2 u
The amount that Albert has at first in Case 1 and Case 2 is the same.
3 u - 15 = 2 u + 20
3 u - 2 u = 20 + 15
1 u = 35
Amount that Albert has
= 2 u + 20
= 2 x 35 + 20
= 70 + 20
= $90
(b)
Amount that Jaslyn has
= 1 u + 15
= 35 + 15
= $50
Answer(s): (a) $90; (b) $50
