Zoe and Ivory had $180. Ivory had $12 more than Zoe. Zoe spent 3 times as much as Ivory and was left with
35 as much as Ivory. How much did Zoe spend more than Ivory?
| |
Make p the same
(1)x5 = (3) |
Zoe
(1) |
Ivory
(2) |
Make p the same
(2)x3 = (4) |
Total
|
Comparing Zoe
and Ivory at first |
|
|
$12 more |
|
$180 |
| Before |
$420 |
$84 |
$96 |
$288 |
|
| Change |
- 15 u |
- 3 u |
- 1 u |
- 3 u |
|
| After |
15 p |
3 p |
5 p |
15 p |
|
Amount that Zoe had at first
= (180 - 12) ÷ 2
= 168 ÷ 2
= $84
Amount that Ivory had at first
= 84 + 12
= $96
84 - 3 u = 3 p --- (1)
96 - 1 u = 5 p --- (2)
Make p the same.
(1)
x 5
420 - 15 u =
15 p --- (3)
(2)
x 3
288 - 3 u =
15 p --- (4)
(4) = (3)
288 - 3 u = 420 - 15 u
15 u - 3 u = 420 - 288
12 u = 132
1 u = 132 ÷ 12 = 11
Amount that Zoe spent more than Ivory
= 3 u - 1 u
= 2 u
= 2 x 11
= $22
Answer(s): $22
