Diana had $180 more than Vanessa. Diana gave
23 of her money to Vanessa. Vanessa then gave 20% of her money to Diana. In the end, Diana had $192 less than Vanessa. How much did Diana have at first?
| |
Diana |
Vanessa |
| Comparing Diana and Vanessa at first |
180 more |
|
| Before |
3 u |
+ 180 |
3 u |
|
| Change 1 |
- 2 u |
- 120 |
+ 2 u |
+ 120 |
| After 1 |
1 u |
+ 60 |
5 u |
+ 120 |
| Change 2 |
+ 1 u |
+ 24 |
- 1 u |
- 24 |
| After 2 |
2 u |
+ 84 |
4 u |
+ 96 |
23 x 180= 120
180 - 120 = 60
20% x 5 u
=
20100 x 5 u
= 1 u
20% x 120
=
20100 x 120
= 24
120 - 24 = 96
60 + 24 = 84
If Diana received another $192 in the end, Diana and Vanessa would have the same amount of money.
4 u + 96 = 2 u + 84 + 192
4 u - 2 u = 84 + 192 - 96
2 u = 180
1 u = 180 ÷ 2 = 90
Amount that Diana had at first
= 3 u + 180
= 3 x 90 + 180
= 270 + 180
= $450
Answer(s): $450
