Dana and Opal had $183. Opal had $27 more than Dana. Dana spent 4 times as much as Opal and was left with
25 as much as Opal. How much did Dana spend more than Opal?
| |
Make p the same
(1)x5 = (3) |
Dana
(1) |
Opal
(2) |
Make p the same
(2)x2 = (4) |
Total
|
Comparing Dana
and Opal at first |
|
|
$27 more |
|
$183 |
| Before |
$390 |
$78 |
$105 |
$210 |
|
| Change |
- 20 u |
- 4 u |
- 1 u |
- 2 u |
|
| After |
10 p |
2 p |
5 p |
10 p |
|
Amount that Dana had at first
= (183 - 27) ÷ 2
= 156 ÷ 2
= $78
Amount that Opal had at first
= 78 + 27
= $105
78 - 4 u = 2 p --- (1)
105 - 1 u = 5 p --- (2)
Make p the same.
(1)
x 5
390 - 20 u =
10 p --- (3)
(2)
x 2
210 - 2 u =
10 p --- (4)
(4) = (3)
210 - 2 u = 390 - 20 u
20 u - 2 u = 390 - 210
18 u = 180
1 u = 180 ÷ 18 = 10
Amount that Dana spent more than Opal
= 4 u - 1 u
= 3 u
= 3 x 10
= $30
Answer(s): $30
