Olivia and Esther had $109. Esther had $5 more than Olivia. Olivia spent 3 times as much as Esther and was left with
23 as much as Esther. How much did Esther spend less than Olivia?
| |
Make p the same
(1) x 3 = (3) |
Olivia
(1) |
Esther
(2) |
Make p the same
(2) x 2 = (4) |
Total
|
Comparing Olivia
and Esther at first |
|
|
$5 more |
|
$109 |
| Before |
$156 |
$52 |
$57 |
$114 |
|
| Change |
- 9 u |
- 3 u |
- 1 u |
- 2 u |
|
| After |
6 p |
2 p |
3 p |
6 p |
|
Amount that Olivia had at first
= (109 - 5) ÷ 2
= 104 ÷ 2
= $52
Amount that Esther had at first
= 52 + 5
= $57
52 - 3 u = 2 p --- (1)
57 - 1 u = 3 p --- (2)
Make p the same.
(1)
x 3
156 - 9 u =
6 p --- (3)
(2)
x 2
114 - 2 u =
6 p --- (4)
(4) = (3)
114 - 2 u = 156 - 9 u
9 u - 2 u = 156 - 114
7 u = 42
1 u = 42 ÷ 7 = 6
Amount that Esther spent less than Olivia
= 3 u - 1 u
= 2 u
= 2 x 6
= $12
Answer(s): $12
