Final answer:
To find the equivalent fraction of 27 out of 90 in terms of x/100, a proportion is set up, and after cross-multiplying and simplifying, the result is x = 30. Therefore, the correct fraction equivalent is 30/100, which can also be represented as 30%.
Step-by-step explanation:
To find the equivalent fraction of 27 out of 90 desserts in terms of x/100, we need to set up a proportion where the total number of desserts corresponds to 100. We are given that 27 desserts are free out of a total of 90. The equivalent fraction would have the same ratio but with a denominator of 100 to represent a percentage.
Setting up the proportion, we have:
27 desserts / 90 desserts = x desserts / 100 desserts
Now we cross-multiply to solve for x:
27 * 100 = 90 * x
2700 = 90x
To find x, we divide both sides by 90:
2700 / 90 = x
x = 30
Therefore, the equivalent fraction of the free desserts is 30/100.