Lucy bought a total of 120 big and small candy canes. Then she decided to exchange 25% of her big candy canes for the small ones in the ratio of 1 : 3. After the exchange, she had 126 candy canes. What percentage of the candy canes she bought were small ones?
| |
Big candy canes |
Small candy canes |
Total |
| Before |
4 u |
? |
120 |
| Change |
- 1 u |
|
|
Comparing big and
small candy canes at exchange |
- 1 u |
+ 3 u |
+ 6 |
| After |
3 u |
? |
126 |
25% =
25100 =
14The number of big candy canes that were exchanged for small candy canes was repeated.
Number of extra candy canes that Lucy received due to the exchange
= 3 u - 1 u
= 2 u
2 u = 126 - 120
2 u = 6
1 u = 6 ÷ 2 = 3
Number of small candy canes at first
= 120 - 4 u
= 120 - 4 x 3
= 120 - 12
= 108
Percentage of the candy canes Lucy bought that were small ones
=
108120 x 100%
= 90%
Answer(s): 90%
