Emma had $360 more than Dana. Emma gave
23 of her money to Dana. Dana then gave 20% of her money to Emma. In the end, Emma had $290 less than Dana. How much did Emma have at first?
| |
Emma |
Dana |
| Comparing Emma and Dana at first |
360 more |
|
| Before |
3 u |
+ 360 |
3 u |
|
| Change 1 |
- 2 u |
- 240 |
+ 2 u |
+ 240 |
| After 1 |
1 u |
+ 120 |
5 u |
+ 240 |
| Change 2 |
+ 1 u |
+ 48 |
- 1 u |
- 48 |
| After 2 |
2 u |
+ 168 |
4 u |
+ 192 |
23 x 360= 240
360 - 240 = 120
20% x 5 u
=
20100 x 5 u
= 1 u
20% x 240
=
20100 x 240
= 48
240 - 48 = 192
120 + 48 = 168
If Emma received another $290 in the end, Emma and Dana would have the same amount of money.
4 u + 192 = 2 u + 168 + 290
4 u - 2 u = 168 + 290 - 192
2 u = 266
1 u = 266 ÷ 2 = 133
Amount that Emma had at first
= 3 u + 360
= 3 x 133 + 360
= 399 + 360
= $759
Answer(s): $759
