Gwen bought a total of 300 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 : 3. After the exchange, she had 312 candy canes. What percentage of the candy canes she bought were small ones?
| |
Big candy canes |
Small candy canes |
Total |
| Before |
2 u |
? |
300 |
| Change |
- 1 u |
|
|
Comparing big and
small candy canes at exchange |
- 1 u |
+ 3 u |
+ 12 |
| After |
1 u |
? |
312 |
50% =
50100 =
12The number of big candy canes that were exchanged for small candy canes was repeated.
Number of extra candy canes that Gwen received due to the exchange
= 3 u - 1 u
= 2 u
2 u = 312 - 300
2 u = 12
1 u = 12 ÷ 2 = 6
Number of small candy canes at first
= 300 - 2 u
= 300 - 2 x 6
= 300 - 12
= 288
Percentage of the candy canes Gwen bought that were small ones
=
288300 x 100%
= 96%
Answer(s): 96%
