Jean and Olivia had $114. Olivia had $6 more than Jean. Jean spent 3 times as much as Olivia and was left with
23 as much as Olivia. How much did Olivia spend less than Jean?
| |
Make p the same
(1) x 3 = (3) |
Jean
(1) |
Olivia
(2) |
Make p the same
(2) x 2 = (4) |
Total
|
Comparing Jean
and Olivia at first |
|
|
$6 more |
|
$114 |
| Before |
$162 |
$54 |
$60 |
$120 |
|
| Change |
- 9 u |
- 3 u |
- 1 u |
- 2 u |
|
| After |
6 p |
2 p |
3 p |
6 p |
|
Amount that Jean had at first
= (114 - 6) ÷ 2
= 108 ÷ 2
= $54
Amount that Olivia had at first
= 54 + 6
= $60
54 - 3 u = 2 p --- (1)
60 - 1 u = 3 p --- (2)
Make p the same.
(1)
x 3
162 - 9 u =
6 p --- (3)
(2)
x 2
120 - 2 u =
6 p --- (4)
(4) = (3)
120 - 2 u = 162 - 9 u
9 u - 2 u = 162 - 120
7 u = 42
1 u = 42 ÷ 7 = 6
Amount that Olivia spent less than Jean
= 3 u - 1 u
= 2 u
= 2 x 6
= $12
Answer(s): $12
