Gwen and Esther had $92. Esther had $4 more than Gwen. Gwen spent 2 times as much as Esther and was left with
23 as much as Esther. How much did Gwen spend?
| |
Make p the same
(1)x3 = (3) |
Gwen
(1) |
Esther
(2) |
Make p the same
(2)x2 = (4) |
Total
|
Comparing Gwen
and Esther at first |
|
|
$4 more |
|
$92 |
| Before |
$132 |
$44 |
$48 |
$96 |
|
| Change |
- 6 u |
- 2 u |
- 1 u |
- 2 u |
|
| After |
6 p |
2 p |
3 p |
6 p |
|
Amount that Gwen had at first
= (92 - 4) ÷ 2
= 88 ÷ 2
= $44
Amount that Esther had at first
= 44 + 4
= $48
44 - 2 u = 2 p --- (1)
48 - 1 u = 3 p --- (2)
Make p the same.
(1)
x 3
132 - 6 u =
6 p --- (3)
(2)
x 2
96 - 2 u =
6 p --- (4)
(4) = (3)
96 - 2 u = 132 - 6 u
6 u - 2 u = 132 - 96
4 u = 36
1 u = 36 ÷ 4 = 9
Amount that Gwen spent
= 2 u
= 2 x 9
= $18
Answer(s): $18
