Hazel and Natalie have some money. If Hazel spends $18, she will have
25 as much money as Natalie. If Natalie spends $20, Hazel will have
56 as much money as Natalie. How much money does Natalie have?
| |
Case 1 |
Case 2 |
| |
Hazel |
Natalie |
Hazel |
Natalie |
| Before |
2 u + $18 |
5 u |
5 p |
6 p + $20 |
| Change |
- $18 |
|
|
- $20 |
| After |
2 u |
5 u |
5 p |
6 p |
The amount that Hazel has at first in Case 1 and Case 2 is the same.
2 u + 18 = 5 p
2 u = 5 p - 18 --- (1)
The amount that Natalie has at first in Case 1 and Case 2 is the same.
5 u = 6 p + 20 --- (2)
Make u the same.
(1)
x 510 u = 25 p - 90 --- (3)
(2)
x 210 u = 12 p + 40 --- (4)
(3) = (4)
25 p - 90 = 12 p + 40
25 p - 12 p = 90 + 40
13 p = 130
1 p = 130 ÷ 13 = 10
Amount that Natalie has
= 6 p + 20
= 6 x 10 + 20
= 60 + 20
= $80
Answer(s): $80
