Vanessa and Barbara have some money. If Vanessa spends $15, she will have
25 as much money as Barbara. If Barbara spends $34, Vanessa will have
56 as much money as Barbara. How much money does Barbara have?
| |
Case 1 |
Case 2 |
| |
Vanessa |
Barbara |
Vanessa |
Barbara |
| Before |
2 u + $15 |
5 u |
5 p |
6 p + $34 |
| Change |
- $15 |
|
|
- $34 |
| After |
2 u |
5 u |
5 p |
6 p |
The amount that Vanessa has at first in Case 1 and Case 2 is the same.
2 u + 15 = 5 p
2 u = 5 p - 15 --- (1)
The amount that Barbara has at first in Case 1 and Case 2 is the same.
5 u = 6 p + 34 --- (2)
Make u the same.
(1)
x 510 u = 25 p - 75 --- (3)
(2)
x 210 u = 12 p + 68 --- (4)
(3) = (4)
25 p - 75 = 12 p + 68
25 p - 12 p = 75 + 68
13 p = 143
1 p = 143 ÷ 13 = 11
Amount that Barbara has
= 6 p + 34
= 6 x 11 + 34
= 66 + 34
= $100
Answer(s): $100
