Olivia had $390 less than Jane. Jane gave
23 of her money to Olivia. Olivia then gave 20% of her money to Jane. In the end, Olivia had $134 more than Jane. How much did Olivia have at first?
| |
Jane |
Olivia |
| Comparing Jane and Olivia at first |
390 more |
|
| Before |
3 u |
+ 390 |
3 u |
|
| Change 1 |
- 2 u |
- 260 |
+ 2 u |
+ 260 |
| After 1 |
1 u |
+ 130 |
5 u |
+ 260 |
| Change 2 |
+ 1 u |
+ 52 |
- 1 u |
- 52 |
| After 2 |
2 u |
+ 182 |
4 u |
+ 208 |
23 x 390= 260
390 - 260 = 130
20% x 5 u
=
20100 x 5 u
= 1 u
20% x 260
=
20100 x 260
= 52
260 - 52 = 208
130 + 52 = 182
If Jane received another $134 in the end, Jane and Olivia would have the same amount of money.
4 u + 208 = 2 u + 182 + 134
4 u - 2 u = 182 + 134 - 208
2 u = 108
1 u = 108 ÷ 2 = 54
Amount that Olivia had at first
= 3 u
= 3 x 54
= $162
Answer(s): $162
