Kathy and Jean had $120. Jean had $4 more than Kathy. Kathy spent 4 times as much as Jean and was left with
23 as much as Jean. How much did Kathy spend?
| |
Make p the same
(1)x3 = (3) |
Kathy
(1) |
Jean
(2) |
Make p the same
(2)x2 = (4) |
Total
|
Comparing Kathy
and Jean at first |
|
|
$4 more |
|
$120 |
| Before |
$174 |
$58 |
$62 |
$124 |
|
| Change |
- 12 u |
- 4 u |
- 1 u |
- 2 u |
|
| After |
6 p |
2 p |
3 p |
6 p |
|
Amount that Kathy had at first
= (120 - 4) ÷ 2
= 116 ÷ 2
= $58
Amount that Jean had at first
= 58 + 4
= $62
58 - 4 u = 2 p --- (1)
62 - 1 u = 3 p --- (2)
Make p the same.
(1)
x 3
174 - 12 u =
6 p --- (3)
(2)
x 2
124 - 2 u =
6 p --- (4)
(4) = (3)
124 - 2 u = 174 - 12 u
12 u - 2 u = 174 - 124
10 u = 50
1 u = 50 ÷ 10 = 5
Amount that Kathy spent
= 4 u
= 4 x 5
= $20
Answer(s): $20
