Jane and Penelope had $109. Penelope had $9 more than Jane. Jane spent 2 times as much as Penelope and was left with
23 as much as Penelope. How much did Jane spend?
| |
Make p the same
(1)x3 = (3) |
Jane
(1) |
Penelope
(2) |
Make p the same
(2)x2 = (4) |
Total
|
Comparing Jane
and Penelope at first |
|
|
$9 more |
|
$109 |
| Before |
$150 |
$50 |
$59 |
$118 |
|
| Change |
- 6 u |
- 2 u |
- 1 u |
- 2 u |
|
| After |
6 p |
2 p |
3 p |
6 p |
|
Amount that Jane had at first
= (109 - 9) ÷ 2
= 100 ÷ 2
= $50
Amount that Penelope had at first
= 50 + 9
= $59
50 - 2 u = 2 p --- (1)
59 - 1 u = 3 p --- (2)
Make p the same.
(1)
x 3
150 - 6 u =
6 p --- (3)
(2)
x 2
118 - 2 u =
6 p --- (4)
(4) = (3)
118 - 2 u = 150 - 6 u
6 u - 2 u = 150 - 118
4 u = 32
1 u = 32 ÷ 4 = 8
Amount that Jane spent
= 2 u
= 2 x 8
= $16
Answer(s): $16
