Rachel bought a total of 100 big and small jelly beans. Then she decided to exchange 20% of her big jelly beans for the small ones in the ratio of 1 : 6. After the exchange, she had 110 jelly beans. What percentage of the jelly beans she bought were small ones?
| |
Big jelly beans |
Small jelly beans |
Total |
| Before |
5 u |
? |
100 |
| Change |
- 1 u |
|
|
Comparing big and
small jelly beans at exchange |
- 1 u |
+ 6 u |
+ 10 |
| After |
4 u |
? |
110 |
20% =
20100 =
15The number of big jelly beans that were exchanged for small jelly beans was repeated.
Number of extra jelly beans that Rachel received due to the exchange
= 6 u - 1 u
= 5 u
5 u = 110 - 100
5 u = 10
1 u = 10 ÷ 5 = 2
Number of small jelly beans at first
= 100 - 5 u
= 100 - 5 x 2
= 100 - 10
= 90
Percentage of the jelly beans Rachel bought that were small ones
=
90100 x 100%
= 90%
Answer(s): 90%
