Penelope had $285 more than Cathy. Penelope gave
23 of her money to Cathy. Cathy then gave 20% of her money to Penelope. In the end, Cathy had $259 more than Penelope. How much did Penelope have at first?
| |
Penelope |
Cathy |
Comparing Penelope
and Cathy at first |
285 more |
|
| Before |
3 u |
+ 285 |
3 u |
|
| Change 1 |
- 2 u |
- 190 |
+ 2 u |
+ 190 |
| After 1 |
1 u |
+ 95 |
5 u |
+ 190 |
| Change 2 |
+ 1 u |
+ 38 |
- 1 u |
- 38 |
| After 2 |
2 u |
+ 133 |
4 u |
+ 152 |
23 x 285= 190
285 - 190 = 95
20% x 5 u
=
20100 x 5 u
= 1 u
20% x 190
=
20100 x 190
= 38
190 - 38 = 152
95 + 38 = 133
If Penelope received another $259 in the end, Penelope and Cathy would have the same amount of money.
4 u + 152 = 2 u + 133 + 259
4 u - 2 u = 133 + 259 - 152
2 u = 240
1 u = 240 ÷ 2 = 120
Amount that Penelope had at first
= 3 u + 285
= 3 x 120 + 285
= 360 + 285
= $645
Answer(s): $645
