Yen and Diana had $168. Diana had $46 more than Yen. Yen spent 3 times as much as Diana and was left with
25 as much as Diana. How much did Diana spend less than Yen?
| |
Make p the same
(1) x 5 = (3) |
Yen
(1) |
Diana
(2) |
Make p the same
(2) x 2 = (4) |
Total
|
Comparing Yen
and Diana at first |
|
|
$46 more |
|
$168 |
| Before |
$305 |
$61 |
$107 |
$214 |
|
| Change |
- 15 u |
- 3 u |
- 1 u |
- 2 u |
|
| After |
10 p |
2 p |
5 p |
10 p |
|
Amount that Yen had at first
= (168 - 46) ÷ 2
= 122 ÷ 2
= $61
Amount that Diana had at first
= 61 + 46
= $107
61 - 3 u = 2 p --- (1)
107 - 1 u = 5 p --- (2)
Make p the same.
(1)
x 5
305 - 15 u =
10 p --- (3)
(2)
x 2
214 - 2 u =
10 p --- (4)
(4) = (3)
214 - 2 u = 305 - 15 u
15 u - 2 u = 305 - 214
13 u = 91
1 u = 91 ÷ 13 = 7
Amount that Diana spent less than Yen
= 3 u - 1 u
= 2 u
= 2 x 7
= $14
Answer(s): $14
