Reggie and Nora has some money each. If Nora gives Reggie $20, he will have 7 times as much money as her. If Reggie gives Nora $19, he will have the same amount of money as her. How much money does each person have respectively?
- Reggie?
- Nora?
| |
Case 1 |
Case 2 |
| |
Reggie |
Nora |
Reggie |
Nora |
| Before |
7 u - 20 |
1 u + 20 |
4 u + 19 |
4 u - 19 |
| Change |
+ 20 |
- 20 |
- 19 |
+ 19 |
| After |
7 u |
1 u |
4 u |
4 u |
(a)
If Nora gives Reggie some money or Reggie gives Nora some money, the total amount of money remains the same.
Total amount that Reggie and Nora have in the end for both cases
= 7 u + 1 u
= 8 u
Amount that Reggie and Nora 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 - 20 = 4 u + 19
7 u - 4 u = 19 + 20
1 u = 39
Amount that Reggie has
= 4 u + 19
= 4 x 39 + 19
= 156 + 19
= $175
(b)
Amount that Nora has
= 1 u + 20
= 39 + 20
= $59
Answer(s): (a) $175; (b) $59
