Natalie and Penelope have some money. If Natalie spends $23, she will have
25 as much money as Penelope. If Penelope spends $14, Natalie will have
56 as much money as Penelope. How much money does Natalie have?
| |
Case 1 |
Case 2 |
| |
Natalie |
Penelope |
Natalie |
Penelope |
| Before |
2 u + $23 |
5 u |
5 p |
6 p + $14 |
| Change |
- $23 |
|
|
- $14 |
| After |
2 u |
5 u |
5 p |
6 p |
The amount that Natalie has at first in Case 1 and Case 2 is the same.
2 u + 23 = 5 p
2 u = 5 p - 23 --- (1)
The amount that Penelope has at first in Case 1 and Case 2 is the same.
5 u = 6 p + 14 --- (2)
Make u the same.
(1)
x 510 u = 25 p - 115 --- (3)
(2)
x 210 u = 12 p + 28 --- (4)
(3) = (4)
25 p - 115 = 12 p + 28
25 p - 12 p = 115 + 28
13 p = 143
1 p = 143 ÷ 13 = 11
Amount that Natalie has
= 5 p
= 5 x 11
= $55
Answer(s): $55
