Diana and Linda have some money. If Diana spends $16, she will have
25 as much money as Linda. If Linda spends $16, Diana will have
67 as much money as Linda. How much money does Linda have?
| |
Case 1 |
Case 2 |
| |
Diana |
Linda |
Diana |
Linda |
| Before |
2 u + $16 |
5 u |
6 p |
7 p + $16 |
| Change |
- $16 |
|
|
- $16 |
| After |
2 u |
5 u |
6 p |
7 p |
The amount that Diana has at first in Case 1 and Case 2 is the same.
2 u + 16 = 6 p
2 u = 6 p - 16 --- (1)
The amount that Linda has at first in Case 1 and Case 2 is the same.
5 u = 7 p + 16 --- (2)
Make u the same.
(1)
x 510 u = 30 p - 80 --- (3)
(2)
x 210 u = 14 p + 32 --- (4)
(3) = (4)
30 p - 80 = 14 p + 32
30 p - 14 p = 80 + 32
16 p = 112
1 p = 112 ÷ 16 = 7
Amount that Linda has
= 7 p + 16
= 7 x 7 + 16
= 49 + 16
= $65
Answer(s): $65
