Fiona bought a total of 120 big and small candy canes. Then she decided to exchange 40% of her big candy canes for the small ones in the ratio of 2 : 5. After the exchange, she had 138 candy canes. What percentage of the candy canes she bought were small ones?
| |
Big candy canes |
Small candy canes |
Total |
| Before |
5 u |
? |
120 |
| Change |
- 2 u |
|
|
Comparing big and
small candy canes at exchange |
- 2 u |
+ 5 u |
+ 18 |
| After |
3 u |
? |
138 |
40% =
40100 =
25The 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 - 2 u
= 3 u
3 u = 138 - 120
3 u = 18
1 u = 18 ÷ 3 = 6
Number of small candy canes at first
= 120 - 5 u
= 120 - 5 x 6
= 120 - 30
= 90
Percentage of the candy canes Fiona bought that were small ones
=
90120 x 100%
= 75%
Answer(s): 75%
