Olivia and Xandra had $115. Xandra had $3 more than Olivia. Olivia spent 4 times as much as Xandra and was left with
23 as much as Xandra. How much did Xandra spend less than Olivia?
| |
Make p the same
(1) x 3 = (3) |
Olivia
(1) |
Xandra
(2) |
Make p the same
(2) x 2 = (4) |
Total
|
Comparing Olivia
and Xandra at first |
|
|
$3 more |
|
$115 |
| Before |
$168 |
$56 |
$59 |
$118 |
|
| Change |
- 12 u |
- 4 u |
- 1 u |
- 2 u |
|
| After |
6 p |
2 p |
3 p |
6 p |
|
Amount that Olivia had at first
= (115 - 3) ÷ 2
= 112 ÷ 2
= $56
Amount that Xandra had at first
= 56 + 3
= $59
56 - 4 u = 2 p --- (1)
59 - 1 u = 3 p --- (2)
Make p the same.
(1)
x 3
168 - 12 u =
6 p --- (3)
(2)
x 2
118 - 2 u =
6 p --- (4)
(4) = (3)
118 - 2 u = 168 - 12 u
12 u - 2 u = 168 - 118
10 u = 50
1 u = 50 ÷ 10 = 5
Amount that Xandra spent less than Olivia
= 4 u - 1 u
= 3 u
= 3 x 5
= $15
Answer(s): $15
