Olivia had $120 less than Vanessa. Vanessa gave
23 of her money to Olivia. Olivia then gave 20% of her money to Vanessa. In the end, Olivia had $184 more than Vanessa. How much did Olivia have at first?
| |
Vanessa |
Olivia |
| Comparing Vanessa 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 Vanessa received another $184 in the end, Vanessa and Olivia would have the same amount of money.
4 u + 64 = 2 u + 56 + 184
4 u - 2 u = 56 + 184 - 64
2 u = 176
1 u = 176 ÷ 2 = 88
Amount that Olivia had at first
= 3 u
= 3 x 88
= $264
Answer(s): $264
