Gem had $300 less than Emily. Emily gave
23 of her money to Gem. Gem then gave 20% of her money to Emily. In the end, Gem had $234 more than Emily. How much did Gem have at first?
| |
Emily |
Gem |
| Comparing Emily and Gem at first |
300 more |
|
| Before |
3 u |
+ 300 |
3 u |
|
| Change 1 |
- 2 u |
- 200 |
+ 2 u |
+ 200 |
| After 1 |
1 u |
+ 100 |
5 u |
+ 200 |
| Change 2 |
+ 1 u |
+ 40 |
- 1 u |
- 40 |
| After 2 |
2 u |
+ 140 |
4 u |
+ 160 |
23 x 300= 200
300 - 200 = 100
20% x 5 u
=
20100 x 5 u
= 1 u
20% x 200
=
20100 x 200
= 40
200 - 40 = 160
100 + 40 = 140
If Emily received another $234 in the end, Emily and Gem would have the same amount of money.
4 u + 160 = 2 u + 140 + 234
4 u - 2 u = 140 + 234 - 160
2 u = 214
1 u = 214 ÷ 2 = 107
Amount that Gem had at first
= 3 u
= 3 x 107
= $321
Answer(s): $321
