Reggie and Jade has some money each. If Jade gives Reggie $17, he will have 7 times as much money as her. If Reggie gives Jade $19, he will have the same amount of money as her. How much money does each person have respectively?
- Reggie?
- Jade?
|
Case 1 |
Case 2 |
|
Reggie |
Jade |
Reggie |
Jade |
Before |
7 u - 17 |
1 u + 17 |
4 u + 19 |
4 u - 19 |
Change |
+ 17 |
- 17 |
- 19 |
+ 19 |
After |
7 u |
1 u |
4 u |
4 u |
(a)
If Jade gives Reggie some money or Reggie gives Jade some money, the total amount of money remains the same.
Total amount that Reggie and Jade have in the end for both cases
= 7 u + 1 u
= 8 u
Amount that Reggie and Jade each has in the end in Case 2
= 8 u ÷ 2
= 4 u
The amount that Reggie has at first in Case 1 and Case 2 is the same.
7 u - 17 = 4 u + 19
7 u - 4 u = 19 + 17
1 u = 36
Amount that Reggie has
= 4 u + 19
= 4 x 36 + 19
= 144 + 19
= $163
(b)
Amount that Jade has
= 1 u + 17
= 36 + 17
= $53
Answer(s): (a) $163; (b) $53