Natalie bought a total of 160 big and small jelly beans. Then she decided to exchange 30% of her big jelly beans for the small ones in the ratio of 3 : 7. After the exchange, she had 176 jelly beans. What percentage of the jelly beans she bought were small ones?
| |
Big jelly beans |
Small jelly beans |
Total |
| Before |
10 u |
? |
160 |
| Change |
- 3 u |
|
|
Comparing big and
small jelly beans at exchange |
- 3 u |
+ 7 u |
+ 16 |
| After |
7 u |
? |
176 |
30% =
30100 =
310The number of big jelly beans that were exchanged for small jelly beans was repeated.
Number of extra jelly beans that Natalie received due to the exchange
= 7 u - 3 u
= 4 u
4 u = 176 - 160
4 u = 16
1 u = 16 ÷ 4 = 4
Number of small jelly beans at first
= 160 - 10 u
= 160 - 10 x 4
= 160 - 40
= 120
Percentage of the jelly beans Natalie bought that were small ones
=
120160 x 100%
= 75%
Answer(s): 75%
