Penelope bought a total of 240 big and small sweets. Then she decided to exchange 60% of her big sweets for the small ones in the ratio of 3 : 7. After the exchange, she had 288 sweets. What percentage of the sweets she bought were small ones?
|
Big sweets |
Small sweets |
Total |
Before |
5 u |
? |
240 |
Change |
- 3 u |
|
|
Comparing big and small sweets at exchange |
- 3 u |
+ 7 u |
+ 48 |
After |
2 u |
? |
288 |
60% =
60100 =
35The number of big sweets that were exchanged for small sweets was repeated.
Number of extra sweets that Penelope received due to the exchange
= 7 u - 3 u
= 4 u
4 u = 288 - 240
4 u = 48
1 u = 48 ÷ 4 = 12
Number of small sweets at first
= 240 - 5 u
= 240 - 5 x 12
= 240 - 60
= 180
Percentage of the sweets Penelope bought that were small ones
=
180240 x 100%
= 75%
Answer(s): 75%