Olivia bought a total of 35 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 : 6. After the exchange, she had 70 candy canes. What percentage of the candy canes she bought were small ones?
| |
Big candy canes |
Small candy canes |
Total |
| Before |
2 u |
? |
35 |
| Change |
- 1 u |
|
|
Comparing big and
small candy canes at exchange |
- 1 u |
+ 6 u |
+ 35 |
| After |
1 u |
? |
70 |
50% =
50100 =
12The number of big candy canes that were exchanged for small candy canes was repeated.
Number of extra candy canes that Olivia received due to the exchange
= 6 u - 1 u
= 5 u
5 u = 70 - 35
5 u = 35
1 u = 35 ÷ 5 = 7
Number of small candy canes at first
= 35 - 2 u
= 35 - 2 x 7
= 35 - 14
= 21
Percentage of the candy canes Olivia bought that were small ones
=
2135 x 100%
= 60%
Answer(s): 60%
