Yen and Cathy had $158. Cathy had $2 more than Yen. Yen spent 3 times as much as Cathy and was left with
34 as much as Cathy. How much did Yen spend more than Cathy?
| |
Make p the same
(1)x4 = (3) |
Yen
(1) |
Cathy
(2) |
Make p the same
(2)x3 = (4) |
Total
|
Comparing Yen
and Cathy at first |
|
|
$2 more |
|
$158 |
| Before |
$312 |
$78 |
$80 |
$240 |
|
| Change |
- 12 u |
- 3 u |
- 1 u |
- 3 u |
|
| After |
12 p |
3 p |
4 p |
12 p |
|
Amount that Yen had at first
= (158 - 2) ÷ 2
= 156 ÷ 2
= $78
Amount that Cathy had at first
= 78 + 2
= $80
78 - 3 u = 3 p --- (1)
80 - 1 u = 4 p --- (2)
Make p the same.
(1)
x 4
312 - 12 u =
12 p --- (3)
(2)
x 3
240 - 3 u =
12 p --- (4)
(4) = (3)
240 - 3 u = 312 - 12 u
12 u - 3 u = 312 - 240
9 u = 72
1 u = 72 ÷ 9 = 8
Amount that Yen spent more than Cathy
= 3 u - 1 u
= 2 u
= 2 x 8
= $16
Answer(s): $16
