Diana had $150 more than Rachel. Diana gave
23 of her money to Rachel. Rachel then gave 20% of her money to Diana. In the end, Rachel had $142 more than Diana. How much did Diana have at first?
| |
Diana |
Rachel |
Comparing Diana
and Rachel at first |
150 more |
|
| Before |
3 u |
+ 150 |
3 u |
|
| Change 1 |
- 2 u |
- 100 |
+ 2 u |
+ 100 |
| After 1 |
1 u |
+ 50 |
5 u |
+ 100 |
| Change 2 |
+ 1 u |
+ 20 |
- 1 u |
- 20 |
| After 2 |
2 u |
+ 70 |
4 u |
+ 80 |
23 x 150= 100
150 - 100 = 50
20% x 5 u
=
20100 x 5 u
= 1 u
20% x 100
=
20100 x 100
= 20
100 - 20 = 80
50 + 20 = 70
If Diana received another $142 in the end, Diana and Rachel would have the same amount of money.
4 u + 80 = 2 u + 70 + 142
4 u - 2 u = 70 + 142 - 80
2 u = 132
1 u = 132 ÷ 2 = 66
Amount that Diana had at first
= 3 u + 150
= 3 x 66 + 150
= 198 + 150
= $348
Answer(s): $348
