Diana and Sarah had $120. Sarah had $10 more than Diana. Diana spent 3 times as much as Sarah and was left with
23 as much as Sarah. How much did Diana spend more than Sarah?
| |
Make p the same
(1)x3 = (3) |
Diana
(1) |
Sarah
(2) |
Make p the same
(2)x2 = (4) |
Total
|
Comparing Diana
and Sarah at first |
|
|
$10 more |
|
$120 |
| Before |
$165 |
$55 |
$65 |
$130 |
|
| Change |
- 9 u |
- 3 u |
- 1 u |
- 2 u |
|
| After |
6 p |
2 p |
3 p |
6 p |
|
Amount that Diana had at first
= (120 - 10) ÷ 2
= 110 ÷ 2
= $55
Amount that Sarah had at first
= 55 + 10
= $65
55 - 3 u = 2 p --- (1)
65 - 1 u = 3 p --- (2)
Make p the same.
(1)
x 3
165 - 9 u =
6 p --- (3)
(2)
x 2
130 - 2 u =
6 p --- (4)
(4) = (3)
130 - 2 u = 165 - 9 u
9 u - 2 u = 165 - 130
7 u = 35
1 u = 35 ÷ 7 = 5
Amount that Diana spent more than Sarah
= 3 u - 1 u
= 2 u
= 2 x 5
= $10
Answer(s): $10
