Cindy bought a total of 180 big and small sweets. Then she decided to exchange 50% of her big sweets for the small ones in the ratio of 1 : 4. After the exchange, she had 207 sweets. What percentage of the sweets she bought were small ones?
| |
Big sweets |
Small sweets |
Total |
| Before |
2 u |
? |
180 |
| Change |
- 1 u |
|
|
Comparing big and
small sweets at exchange |
- 1 u |
+ 4 u |
+ 27 |
| After |
1 u |
? |
207 |
50% =
50100 =
12The number of big sweets that were exchanged for small sweets was repeated.
Number of extra sweets that Cindy received due to the exchange
= 4 u - 1 u
= 3 u
3 u = 207 - 180
3 u = 27
1 u = 27 ÷ 3 = 9
Number of small sweets at first
= 180 - 2 u
= 180 - 2 x 9
= 180 - 18
= 162
Percentage of the sweets Cindy bought that were small ones
=
162180 x 100%
= 90%
Answer(s): 90%
