Hazel, Nora and Gabby had 1296 stickers. Nora won some of the stickers from Hazel and as a result, Nora's stickers increased by 25%. Gabby then won some stickers from Nora and Gabby's stickers increased by 50%. Finally, Gabby lost some of her stickers to Hazel and Hazel's stickers increased by 20%. In the end, they realised that they each had an equal number of stickers. How many percent less did Hazel have in the end than what she had at first? Correct your answer to 1 decimal place.
Hazel |
Nora |
Gabby |
1296 |
|
4 u |
|
- 1 u |
+ 1 u |
|
|
5 u |
|
|
|
2 p |
|
- 1 p |
+ 1 p |
|
|
3 p |
5 boxes |
|
|
+ 1 box |
|
- 1 box |
6 boxes |
|
|
1 group |
1 group |
1 group |
25% =
25100 =
1450% =
50100 =
1220% =
20100 =
15Working backwards.
3 groups = 1296
1 group = 1296 ÷ 3 = 432
1 group = 6 boxes
6 boxes = 432
1 box = 432 ÷ 6 = 72
1 group + 1 box = 3 p
432 + 72 = 3 p
3 p = 504
1 p = 504 ÷ 3 = 168
1 p = 1 x 168 = 168
1 group + 1 p = 5 u
432 + 168 = 5 u
5 u = 600
1 u = 600 ÷ 5 = 120
Number of stickers that Hazel had at first
= 5 boxes + 1 u
= (5 x 72) + 120
= 360 + 120
= 480
Percent that Hazel had less in the end than at first
=
480 - 432480 x 100%
≈ 10.0%
Answer(s): 10.0%