Betty bought a total of 480 big and small sweets. Then she decided to exchange 50% of her big sweets for the small ones in the ratio of 1 : 3. After the exchange, she had 504 sweets. What percentage of the sweets she bought were small ones?
| |
Big sweets |
Small sweets |
Total |
| Before |
2 u |
? |
480 |
| Change |
- 1 u |
|
|
Comparing big and
small sweets at exchange |
- 1 u |
+ 3 u |
+ 24 |
| After |
1 u |
? |
504 |
50% =
50100 =
12The number of big sweets that were exchanged for small sweets was repeated.
Number of extra sweets that Betty received due to the exchange
= 3 u - 1 u
= 2 u
2 u = 504 - 480
2 u = 24
1 u = 24 ÷ 2 = 12
Number of small sweets at first
= 480 - 2 u
= 480 - 2 x 12
= 480 - 24
= 456
Percentage of the sweets Betty bought that were small ones
=
456480 x 100%
= 95%
Answer(s): 95%
