Barbara and Mary have some money. If Barbara spends $29, she will have
25 as much money as Mary. If Mary spends $12, Barbara will have
56 as much money as Mary. How much money does Barbara have?
| |
Case 1 |
Case 2 |
| |
Barbara |
Mary |
Barbara |
Mary |
| Before |
2 u + $29 |
5 u |
5 p |
6 p + $12 |
| Change |
- $29 |
|
|
- $12 |
| After |
2 u |
5 u |
5 p |
6 p |
The amount that Barbara has at first in Case 1 and Case 2 is the same.
2 u + 29 = 5 p
2 u = 5 p - 29 --- (1)
The amount that Mary has at first in Case 1 and Case 2 is the same.
5 u = 6 p + 12 --- (2)
Make u the same.
(1)
x 510 u = 25 p - 145 --- (3)
(2)
x 210 u = 12 p + 24 --- (4)
(3) = (4)
25 p - 145 = 12 p + 24
25 p - 12 p = 145 + 24
13 p = 169
1 p = 169 ÷ 13 = 13
Amount that Barbara has
= 5 p
= 5 x 13
= $65
Answer(s): $65
