Usha, Jaslyn and Jane had 1080 cards. Jaslyn won some of the cards from Usha and as a result, Jaslyn's cards increased by 25%. Jane then won some cards from Jaslyn and Jane's cards increased by 40%. Finally, Jane lost some of her cards to Usha and Usha's cards increased by 20%. In the end, they realised that they each had an equal number of cards. How many percent less did Usha have in the end than what she had at first? Correct your answer to 1 decimal place.
Usha |
Jaslyn |
Jane |
1080 |
|
4 u |
|
- 1 u |
+ 1 u |
|
|
5 u |
|
|
|
5 p |
|
- 2 p |
+ 2 p |
|
|
7 p |
5 boxes |
|
|
+ 1 box |
|
- 1 box |
6 boxes |
|
|
1 group |
1 group |
1 group |
25% =
25100 =
1440% =
40100 =
2520% =
20100 =
15Working backwards.
3 groups = 1080
1 group = 1080 ÷ 3 = 360
1 group = 6 boxes
6 boxes = 360
1 box = 360 ÷ 6 = 60
1 group + 1 box = 7 p
360 + 60 = 7 p
7 p = 420
1 p = 420 ÷ 7 = 60
2 p = 2 x 60 = 120
1 group + 2 p = 5 u
360 + 120 = 5 u
5 u = 480
1 u = 480 ÷ 5 = 96
Number of cards that Usha had at first
= 5 boxes + 1 u
= (5 x 60) + 96
= 300 + 96
= 396
Percent that Usha had less in the end than at first
=
396 - 360396 x 100%
≈ 9.1%
Answer(s): 9.1%