Jen and Cathy had $105. Cathy had $1 more than Jen. Jen spent 4 times as much as Cathy and was left with
23 as much as Cathy. How much did Cathy spend less than Jen?
| |
Make p the same
(1) x 3 = (3) |
Jen
(1) |
Cathy
(2) |
Make p the same
(2) x 2 = (4) |
Total
|
Comparing Jen
and Cathy at first |
|
|
$1 more |
|
$105 |
| Before |
$156 |
$52 |
$53 |
$106 |
|
| Change |
- 12 u |
- 4 u |
- 1 u |
- 2 u |
|
| After |
6 p |
2 p |
3 p |
6 p |
|
Amount that Jen had at first
= (105 - 1) ÷ 2
= 104 ÷ 2
= $52
Amount that Cathy had at first
= 52 + 1
= $53
52 - 4 u = 2 p --- (1)
53 - 1 u = 3 p --- (2)
Make p the same.
(1)
x 3
156 - 12 u =
6 p --- (3)
(2)
x 2
106 - 2 u =
6 p --- (4)
(4) = (3)
106 - 2 u = 156 - 12 u
12 u - 2 u = 156 - 106
10 u = 50
1 u = 50 ÷ 10 = 5
Amount that Cathy spent less than Jen
= 4 u - 1 u
= 3 u
= 3 x 5
= $15
Answer(s): $15
