Olivia had $120 less than Gillian. Gillian gave
23 of her money to Olivia. Olivia then gave 20% of her money to Gillian. In the end, Gillian had $162 less than Olivia. How much did Olivia have at first?
| |
Gillian |
Olivia |
| Comparing Gillian and Olivia at first |
120 more |
|
| Before |
3 u |
+ 120 |
3 u |
|
| Change 1 |
- 2 u |
- 80 |
+ 2 u |
+ 80 |
| After 1 |
1 u |
+ 40 |
5 u |
+ 80 |
| Change 2 |
+ 1 u |
+ 16 |
- 1 u |
- 16 |
| After 2 |
2 u |
+ 56 |
4 u |
+ 64 |
23 x 120= 80
120 - 80 = 40
20% x 5 u
=
20100 x 5 u
= 1 u
20% x 80
=
20100 x 80
= 16
80 - 16 = 64
40 + 16 = 56
If Gillian received another $162 in the end, Gillian and Olivia would have the same amount of money.
4 u + 64 = 2 u + 56 + 162
4 u - 2 u = 56 + 162 - 64
2 u = 154
1 u = 154 ÷ 2 = 77
Amount that Olivia had at first
= 3 u
= 3 x 77
= $231
Answer(s): $231
