Victoria bought a total of 160 big and small sweets. Then she decided to exchange 40% of her big sweets for the small ones in the ratio of 2 : 5. After the exchange, she had 184 sweets. What percentage of the sweets she bought were small ones?
|
Big sweets |
Small sweets |
Total |
Before |
5 u |
? |
160 |
Change |
- 2 u |
|
|
Comparing big and small sweets at exchange |
- 2 u |
+ 5 u |
+ 24 |
After |
3 u |
? |
184 |
40% =
40100 =
25The number of big sweets that were exchanged for small sweets was repeated.
Number of extra sweets that Victoria received due to the exchange
= 5 u - 2 u
= 3 u
3 u = 184 - 160
3 u = 24
1 u = 24 ÷ 3 = 8
Number of small sweets at first
= 160 - 5 u
= 160 - 5 x 8
= 160 - 40
= 120
Percentage of the sweets Victoria bought that were small ones
=
120160 x 100%
= 75%
Answer(s): 75%