Betty bought a total of 200 big and small candy canes. Then she decided to exchange 50% of her big candy canes for the small ones in the ratio of 1 : 4. After the exchange, she had 224 candy canes. What percentage of the candy canes she bought were small ones?
|
Big candy canes |
Small candy canes |
Total |
Before |
2 u |
? |
200 |
Change |
- 1 u |
|
|
Comparing big and small candy canes at exchange |
- 1 u |
+ 4 u |
+ 24 |
After |
1 u |
? |
224 |
50% =
50100 =
12The number of big candy canes that were exchanged for small candy canes was repeated.
Number of extra candy canes that Betty received due to the exchange
= 4 u - 1 u
= 3 u
3 u = 224 - 200
3 u = 24
1 u = 24 ÷ 3 = 8
Number of small candy canes at first
= 200 - 2 u
= 200 - 2 x 8
= 200 - 16
= 184
Percentage of the candy canes Betty bought that were small ones
=
184200 x 100%
= 92%
Answer(s): 92%