Diana had $400 more than Emily. Diana gave
35 of her money to Emily. Emily then gave 25% of her money to Diana. In the end, Emily had $114 more than Diana. How much did Diana have at first?
| |
Diana |
Emily |
Comparing Diana
and Emily at first |
400 more |
|
| Before |
5 u |
+ 400 |
5 u |
|
| Change 1 |
- 3 u |
- 240 |
+ 3 u |
+ 240 |
| After 1 |
2 u |
+ 160 |
8 u |
+ 240 |
| Change 2 |
+ 2 u |
+ 60 |
- 2 u |
- 60 |
| After 2 |
4 u |
+ 220 |
6 u |
+ 180 |
35 x 400= 240
400 - 240 = 160
25% x 8 u
=
25100 x 8 u
= 2 u
25% x 240
=
25100 x 240
= 60
240 - 60 = 180
160 + 60 = 220
If Diana received another $114 in the end, Diana and Emily would have the same amount of money.
6 u + 180 = 4 u + 220 + 114
6 u - 4 u = 220 + 114 - 180
2 u = 154
1 u = 154 ÷ 2 = 77
Amount that Diana had at first
= 5 u + 400
= 5 x 77 + 400
= 385 + 400
= $785
Answer(s): $785
