Fiona bought a total of 200 big and small jelly beans. Then she decided to exchange 50% of her big jelly beans for the small ones in the ratio of 1 : 3. After the exchange, she had 216 jelly beans. What percentage of the jelly beans she bought were small ones?
|
Big jelly beans |
Small jelly beans |
Total |
Before |
2 u |
? |
200 |
Change |
- 1 u |
|
|
Comparing big and small jelly beans at exchange |
- 1 u |
+ 3 u |
+ 16 |
After |
1 u |
? |
216 |
50% =
50100 =
12The number of big jelly beans that were exchanged for small jelly beans was repeated.
Number of extra jelly beans that Fiona received due to the exchange
= 3 u - 1 u
= 2 u
2 u = 216 - 200
2 u = 16
1 u = 16 ÷ 2 = 8
Number of small jelly beans at first
= 200 - 2 u
= 200 - 2 x 8
= 200 - 16
= 184
Percentage of the jelly beans Fiona bought that were small ones
=
184200 x 100%
= 92%
Answer(s): 92%