Ahmad and Jen has some money each. If Jen gives Ahmad $16, he will have 3 times as much money as her. If Ahmad gives Jen $19, he will have the same amount of money as her. How much money does each person have respectively?
- Ahmad?
- Jen?
| |
Case 1 |
Case 2 |
| |
Ahmad |
Jen |
Ahmad |
Jen |
| Before |
3 u - 16 |
1 u + 16 |
2 u + 19 |
2 u - 19 |
| Change |
+ 16 |
- 16 |
- 19 |
+ 19 |
| After |
3 u |
1 u |
2 u |
2 u |
(a)
If Jen gives Ahmad some money or Ahmad gives Jen some money, the total amount of money remains the same.
Total amount that Ahmad and Jen have in the end for both cases
= 3 u + 1 u
= 4 u
Amount that Ahmad and Jen each has in the end in Case 2
= 4 u ÷ 2
= 2 u
The amount that Ahmad has at first in Case 1 and Case 2 is the same.
3 u - 16 = 2 u + 19
3 u - 2 u = 19 + 16
1 u = 35
Amount that Ahmad has
= 2 u + 19
= 2 x 35 + 19
= 70 + 19
= $89
(b)
Amount that Jen has
= 1 u + 16
= 35 + 16
= $51
Answer(s): (a) $89; (b) $51
