Fiona bought a total of 100 big and small candy canes. Then she decided to exchange 75% of her big candy canes for the small ones in the ratio of 3 : 5. After the exchange, she had 108 candy canes. What percentage of the candy canes she bought were small ones?
| |
Big candy canes |
Small candy canes |
Total |
| Before |
4 u |
? |
100 |
| Change |
- 3 u |
|
|
Comparing big and
small candy canes at exchange |
- 3 u |
+ 5 u |
+ 8 |
| After |
1 u |
? |
108 |
75% =
75100 =
34The number of big candy canes that were exchanged for small candy canes was repeated.
Number of extra candy canes that Fiona received due to the exchange
= 5 u - 3 u
= 2 u
2 u = 108 - 100
2 u = 8
1 u = 8 ÷ 2 = 4
Number of small candy canes at first
= 100 - 4 u
= 100 - 4 x 4
= 100 - 16
= 84
Percentage of the candy canes Fiona bought that were small ones
=
84100 x 100%
= 84%
Answer(s): 84%
