Barbara and Cathy had $192. Cathy had $24 more than Barbara. Barbara spent 3 times as much as Cathy and was left with
35 as much as Cathy. How much did Barbara spend more than Cathy?
| |
Make p the same
(1)x5 = (3) |
Barbara
(1) |
Cathy
(2) |
Make p the same
(2)x3 = (4) |
Total
|
Comparing Barbara
and Cathy at first |
|
|
$24 more |
|
$192 |
| Before |
$420 |
$84 |
$108 |
$324 |
|
| Change |
- 15 u |
- 3 u |
- 1 u |
- 3 u |
|
| After |
15 p |
3 p |
5 p |
15 p |
|
Amount that Barbara had at first
= (192 - 24) ÷ 2
= 168 ÷ 2
= $84
Amount that Cathy had at first
= 84 + 24
= $108
84 - 3 u = 3 p --- (1)
108 - 1 u = 5 p --- (2)
Make p the same.
(1)
x 5
420 - 15 u =
15 p --- (3)
(2)
x 3
324 - 3 u =
15 p --- (4)
(4) = (3)
324 - 3 u = 420 - 15 u
15 u - 3 u = 420 - 324
12 u = 96
1 u = 96 ÷ 12 = 8
Amount that Barbara spent more than Cathy
= 3 u - 1 u
= 2 u
= 2 x 8
= $16
Answer(s): $16
