Emma had $435 more than Betty. Emma gave
23 of her money to Betty. Betty then gave 20% of her money to Emma. In the end, Emma had $297 less than Betty. How much did Emma have at first?
| |
Emma |
Betty |
| Comparing Emma and Betty at first |
435 more |
|
| Before |
3 u |
+ 435 |
3 u |
|
| Change 1 |
- 2 u |
- 290 |
+ 2 u |
+ 290 |
| After 1 |
1 u |
+ 145 |
5 u |
+ 290 |
| Change 2 |
+ 1 u |
+ 58 |
- 1 u |
- 58 |
| After 2 |
2 u |
+ 203 |
4 u |
+ 232 |
23 x 435= 290
435 - 290 = 145
20% x 5 u
=
20100 x 5 u
= 1 u
20% x 290
=
20100 x 290
= 58
290 - 58 = 232
145 + 58 = 203
If Emma received another $297 in the end, Emma and Betty would have the same amount of money.
4 u + 232 = 2 u + 203 + 297
4 u - 2 u = 203 + 297 - 232
2 u = 268
1 u = 268 ÷ 2 = 134
Amount that Emma had at first
= 3 u + 435
= 3 x 134 + 435
= 402 + 435
= $837
Answer(s): $837
