Gwen and Anna had $180. Anna had $18 more than Gwen. Gwen spent 3 times as much as Anna and was left with
35 as much as Anna. How much did Gwen spend more than Anna?
| |
Make p the same
(1)x5 = (3) |
Gwen
(1) |
Anna
(2) |
Make p the same
(2)x3 = (4) |
Total
|
Comparing Gwen
and Anna at first |
|
|
$18 more |
|
$180 |
| Before |
$405 |
$81 |
$99 |
$297 |
|
| Change |
- 15 u |
- 3 u |
- 1 u |
- 3 u |
|
| After |
15 p |
3 p |
5 p |
15 p |
|
Amount that Gwen had at first
= (180 - 18) ÷ 2
= 162 ÷ 2
= $81
Amount that Anna had at first
= 81 + 18
= $99
81 - 3 u = 3 p --- (1)
99 - 1 u = 5 p --- (2)
Make p the same.
(1)
x 5
405 - 15 u =
15 p --- (3)
(2)
x 3
297 - 3 u =
15 p --- (4)
(4) = (3)
297 - 3 u = 405 - 15 u
15 u - 3 u = 405 - 297
12 u = 108
1 u = 108 ÷ 12 = 9
Amount that Gwen spent more than Anna
= 3 u - 1 u
= 2 u
= 2 x 9
= $18
Answer(s): $18
