Three girls, Gem, Jade and Elyse had a total of 4560 erasers. Some exchanges were made. First, Gem gave Jade as many erasers as Jade had. After that, Jade gave
13 of whatever she had then to Elyse. Finally, Elyse gave
13 of whatever she had to Gem. As a result, they each had the same number of erasers. How many erasers did Gem have at first?
|
Gem |
Jade |
Elyse |
Total |
Before 1 |
? |
1 u |
|
4560 |
Change 1 |
- 1 u |
+ 1 u |
|
|
After 1 |
|
2 u |
|
|
Before 2 |
|
3 p |
|
4560 |
Change 2 |
|
- 1 p |
+ 1 p |
|
After 2 |
|
2 p |
|
|
Before 3 |
|
|
3 boxes |
4560 |
Change 3 |
+ 1 box |
|
- 1 box |
|
After 3 |
|
|
2 boxes |
|
After 3 |
1 group |
1 group |
1 group |
4560 |
3 groups = 4560
1 group = 4560 ÷ 3 = 1520
1 group = 2 boxes 2 boxes = 1520
1 box = 1520 ÷ 2 = 760
2 p = 1 group
1 p = 1520 ÷ 2 = 760
3 p = 3 x 760 = 2280
3 p = 2 u
2 u = 2280
1 u = 2280 ÷ 2 = 1140
Number of erasers that Gem had at first
= 1 group - 1 box + 1 u
= 1520 - 760 + 1140
= 1900
Answer(s): 1900