Joelle bought a total of 70 big and small sweets. Then she decided to exchange 50% of her big sweets for the small ones in the ratio of 1 : 6. After the exchange, she had 105 sweets. What percentage of the sweets she bought were small ones?
|
Big sweets |
Small sweets |
Total |
Before |
2 u |
? |
70 |
Change |
- 1 u |
|
|
Comparing big and small sweets at exchange |
- 1 u |
+ 6 u |
+ 35 |
After |
1 u |
? |
105 |
50% =
50100 =
12The number of big sweets that were exchanged for small sweets was repeated.
Number of extra sweets that Joelle received due to the exchange
= 6 u - 1 u
= 5 u
5 u = 105 - 70
5 u = 35
1 u = 35 ÷ 5 = 7
Number of small sweets at first
= 70 - 2 u
= 70 - 2 x 7
= 70 - 14
= 56
Percentage of the sweets Joelle bought that were small ones
=
5670 x 100%
= 80%
Answer(s): 80%