Diana and Fiona had $129. Fiona had $33 more than Diana. Diana spent 3 times as much as Fiona and was left with
25 as much as Fiona. How much did Diana spend more than Fiona?
| |
Make p the same
(1)x5 = (3) |
Diana
(1) |
Fiona
(2) |
Make p the same
(2)x2 = (4) |
Total
|
Comparing Diana
and Fiona at first |
|
|
$33 more |
|
$129 |
| Before |
$240 |
$48 |
$81 |
$162 |
|
| Change |
- 15 u |
- 3 u |
- 1 u |
- 2 u |
|
| After |
10 p |
2 p |
5 p |
10 p |
|
Amount that Diana had at first
= (129 - 33) ÷ 2
= 96 ÷ 2
= $48
Amount that Fiona had at first
= 48 + 33
= $81
48 - 3 u = 2 p --- (1)
81 - 1 u = 5 p --- (2)
Make p the same.
(1)
x 5
240 - 15 u =
10 p --- (3)
(2)
x 2
162 - 2 u =
10 p --- (4)
(4) = (3)
162 - 2 u = 240 - 15 u
15 u - 2 u = 240 - 162
13 u = 78
1 u = 78 ÷ 13 = 6
Amount that Diana spent more than Fiona
= 3 u - 1 u
= 2 u
= 2 x 6
= $12
Answer(s): $12
