Gem had $480 less than Kathy. Kathy gave
23 of her money to Gem. Gem then gave 20% of her money to Kathy. In the end, Gem had $272 more than Kathy. How much did Gem have at first?
| |
Kathy |
Gem |
| Comparing Kathy and Gem at first |
480 more |
|
| Before |
3 u |
+ 480 |
3 u |
|
| Change 1 |
- 2 u |
- 320 |
+ 2 u |
+ 320 |
| After 1 |
1 u |
+ 160 |
5 u |
+ 320 |
| Change 2 |
+ 1 u |
+ 64 |
- 1 u |
- 64 |
| After 2 |
2 u |
+ 224 |
4 u |
+ 256 |
23 x 480= 320
480 - 320 = 160
20% x 5 u
=
20100 x 5 u
= 1 u
20% x 320
=
20100 x 320
= 64
320 - 64 = 256
160 + 64 = 224
If Kathy received another $272 in the end, Kathy and Gem would have the same amount of money.
4 u + 256 = 2 u + 224 + 272
4 u - 2 u = 224 + 272 - 256
2 u = 240
1 u = 240 ÷ 2 = 120
Amount that Gem had at first
= 3 u
= 3 x 120
= $360
Answer(s): $360
