Fiona bought a total of 40 big and small candy canes. Then she decided to exchange 80% of her big candy canes for the small ones in the ratio of 4 : 7. After the exchange, she had 46 candy canes. What percentage of the candy canes she bought were small ones?
| |
Big candy canes |
Small candy canes |
Total |
| Before |
5 u |
? |
40 |
| Change |
- 4 u |
|
|
Comparing big and
small candy canes at exchange |
- 4 u |
+ 7 u |
+ 6 |
| After |
1 u |
? |
46 |
80% =
80100 =
45The 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
= 7 u - 4 u
= 3 u
3 u = 46 - 40
3 u = 6
1 u = 6 ÷ 3 = 2
Number of small candy canes at first
= 40 - 5 u
= 40 - 5 x 2
= 40 - 10
= 30
Percentage of the candy canes Fiona bought that were small ones
=
3040 x 100%
= 75%
Answer(s): 75%
