Olivia had $300 more than Emma. Olivia gave
35 of her money to Emma. Emma then gave 25% of her money to Olivia. In the end, Olivia had $214 less than Emma. How much did Olivia have at first?
| |
Olivia |
Emma |
| Comparing Olivia and Emma at first |
300 more |
|
| Before |
5 u |
+ 300 |
5 u |
|
| Change 1 |
- 3 u |
- 180 |
+ 3 u |
+ 180 |
| After 1 |
2 u |
+ 120 |
8 u |
+ 180 |
| Change 2 |
+ 2 u |
+ 45 |
- 2 u |
- 45 |
| After 2 |
4 u |
+ 165 |
6 u |
+ 135 |
35 x 300= 180
300 - 180 = 120
25% x 8 u
=
25100 x 8 u
= 2 u
25% x 180
=
25100 x 180
= 45
180 - 45 = 135
120 + 45 = 165
If Olivia received another $214 in the end, Olivia and Emma would have the same amount of money.
6 u + 135 = 4 u + 165 + 214
6 u - 4 u = 165 + 214 - 135
2 u = 244
1 u = 244 ÷ 2 = 122
Amount that Olivia had at first
= 5 u + 300
= 5 x 122 + 300
= 610 + 300
= $910
Answer(s): $910
