Albert and Gabby has some money each. If Gabby gives Albert $10, he will have 3 times as much money as her. If Albert gives Gabby $12, he will have the same amount of money as her. How much money does each person have respectively?
- Albert?
- Gabby?
| |
Case 1 |
Case 2 |
| |
Albert |
Gabby |
Albert |
Gabby |
| Before |
3 u - 10 |
1 u + 10 |
2 u + 12 |
2 u - 12 |
| Change |
+ 10 |
- 10 |
- 12 |
+ 12 |
| After |
3 u |
1 u |
2 u |
2 u |
(a)
If Gabby gives Albert some money or Albert gives Gabby some money, the total amount of money remains the same.
Total amount that Albert and Gabby have in the end for both cases
= 3 u + 1 u
= 4 u
Amount that Albert and Gabby 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 - 10 = 2 u + 12
3 u - 2 u = 12 + 10
1 u = 22
Amount that Albert has
= 2 u + 12
= 2 x 22 + 12
= 44 + 12
= $56
(b)
Amount that Gabby has
= 1 u + 10
= 22 + 10
= $32
Answer(s): (a) $56; (b) $32
