Michael and Gabby has some money each. If Gabby gives Michael $10, he will have 3 times as much money as her. If Michael gives Gabby $16, he will have the same amount of money as her. How much money does each person have respectively?
- Michael?
- Gabby?
| |
Case 1 |
Case 2 |
| |
Michael |
Gabby |
Michael |
Gabby |
| Before |
3 u - 10 |
1 u + 10 |
2 u + 16 |
2 u - 16 |
| Change |
+ 10 |
- 10 |
- 16 |
+ 16 |
| After |
3 u |
1 u |
2 u |
2 u |
(a)
If Gabby gives Michael some money or Michael gives Gabby some money, the total amount of money remains the same.
Total amount that Michael and Gabby have in the end for both cases
= 3 u + 1 u
= 4 u
Amount that Michael and Gabby each has in the end in Case 2
= 4 u ÷ 2
= 2 u
The amount that Michael has at first in Case 1 and Case 2 is the same.
3 u - 10 = 2 u + 16
3 u - 2 u = 16 + 10
1 u = 26
Amount that Michael has
= 2 u + 16
= 2 x 26 + 16
= 52 + 16
= $68
(b)
Amount that Gabby has
= 1 u + 10
= 26 + 10
= $36
Answer(s): (a) $68; (b) $36
