Three girls, Gwen, Tammy and Tina had a total of 1320 erasers. Some exchanges were made. First, Gwen gave Tammy as many erasers as Tammy had. After that, Tammy gave
13 of whatever she had then to Tina. Finally, Tina gave
13 of whatever she had to Gwen. As a result, they each had the same number of erasers. How many erasers did Gwen have at first?
|
Gwen |
Tammy |
Tina |
Total |
Before 1 |
? |
1 u |
|
1320 |
Change 1 |
- 1 u |
+ 1 u |
|
|
After 1 |
|
2 u |
|
|
Before 2 |
|
3 p |
|
1320 |
Change 2 |
|
- 1 p |
+ 1 p |
|
After 2 |
|
2 p |
|
|
Before 3 |
|
|
3 boxes |
1320 |
Change 3 |
+ 1 box |
|
- 1 box |
|
After 3 |
|
|
2 boxes |
|
After 3 |
1 group |
1 group |
1 group |
1320 |
3 groups = 1320
1 group = 1320 ÷ 3 = 440
1 group = 2 boxes 2 boxes = 440
1 box = 440 ÷ 2 = 220
2 p = 1 group
1 p = 440 ÷ 2 = 220
3 p = 3 x 220 = 660
3 p = 2 u
2 u = 660
1 u = 660 ÷ 2 = 330
Number of erasers that Gwen had at first
= 1 group - 1 box + 1 u
= 440 - 220 + 330
= 550
Answer(s): 550