Elyse and Nora have some money. If Elyse spends $14, she will have
25 as much money as Nora. If Nora spends $5, Elyse will have
67 as much money as Nora. How much money does Nora have?
| |
Case 1 |
Case 2 |
| |
Elyse |
Nora |
Elyse |
Nora |
| Before |
2 u + $14 |
5 u |
6 p |
7 p + $5 |
| Change |
- $14 |
|
|
- $5 |
| After |
2 u |
5 u |
6 p |
7 p |
The amount that Elyse has at first in Case 1 and Case 2 is the same.
2 u + 14 = 6 p
2 u = 6 p - 14 --- (1)
The amount that Nora has at first in Case 1 and Case 2 is the same.
5 u = 7 p + 5 --- (2)
Make u the same.
(1)
x 510 u = 30 p - 70 --- (3)
(2)
x 210 u = 14 p + 10 --- (4)
(3) = (4)
30 p - 70 = 14 p + 10
30 p - 14 p = 70 + 10
16 p = 80
1 p = 80 ÷ 16 = 5
Amount that Nora has
= 7 p + 5
= 7 x 5 + 5
= 35 + 5
= $40
Answer(s): $40
