Natalie and Opal have some money. If Natalie spends $3, she will have
34 as much money as Opal. If Opal spends $8, Natalie will have
78 as much money as Opal. How much money does Opal have?
| |
Case 1 |
Case 2 |
| |
Natalie |
Opal |
Natalie |
Opal |
| Before |
3 u + $3 |
4 u |
7 p |
8 p + $8 |
| Change |
- $3 |
|
|
- $8 |
| After |
3 u |
4 u |
7 p |
8 p |
The amount that Natalie has at first in Case 1 and Case 2 is the same.
3 u + 3 = 7 p
3 u = 7 p - 3 --- (1)
The amount that Opal has at first in Case 1 and Case 2 is the same.
4 u = 8 p + 8 --- (2)
Make u the same.
(1)
x 412 u = 28 p - 12 --- (3)
(2)
x 312 u = 24 p + 24 --- (4)
(3) = (4)
28 p - 12 = 24 p + 24
28 p - 24 p = 12 + 24
4 p = 36
1 p = 36 ÷ 4 = 9
Amount that Opal has
= 8 p + 8
= 8 x 9 + 8
= 72 + 8
= $80
Answer(s): $80
