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In a bakery, \(\frac{3}{4}\) of all the cakes are either cheesecake or carrot cake. The cheesecakes make up \(\frac{2}{5}\) of all the cakes. What fraction of all the cakes are carrot cakes?

Answer :

Using proportions, it is found that the fraction of all the cakes are carrot cakes is of [tex]\frac{7}{20}[/tex].

What is a proportion?

A proportion is a fraction of a total amount.

In this problem, we have that:

  • 3/4 of the cakes are either cheesecakes or carrot cakes.
  • 2/5 of the cakes are cheesecakes.
  • The fraction corresponding to carrot cakes is x.

Hence:

[tex]\frac{2}{5} + x = \frac{3}{4}[/tex]

[tex]\frac{2 + 5x}{5} = \frac{3}{4}[/tex]

[tex]8 + 20x = 15[/tex]

[tex]20x = 7[/tex]

[tex]x = \frac{7}{20}[/tex]

The fraction of all the cakes are carrot cakes is of [tex]\frac{7}{20}[/tex].

More can be learned about proportions at https://brainly.com/question/24372153

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Rewritten by : Barada

Final answer:

To determine the fraction of carrot cakes among all cakes in a bakery where 3/4 are cheesecake or carrot cake, and cheesecakes constitute 2/5 of all cakes, we subtract the latter from the former to get 7/20 cakes as carrot cakes.

Explanation:

The student asks what fraction of all the cakes in a bakery are carrot cakes if 3/4 of all cakes are either cheesecakes or carrot cakes, and cheesecakes make up 2/5 of all the cakes. To find out the fraction of carrot cakes, first determine what fraction of all cakes are cheesecakes and then subtract this from the total fraction of cakes that are cheesecake or carrot cake combined.

Step-by-Step Explanation:

Calculate the fraction of cheesecakes. Since cheesecakes make up 2/5 of all cakes, you have this fraction directly.

Understand that the total fraction of cheesecake and carrot cake is 3/4 of all the cakes. This means that to find the fraction of carrot cakes, you need to subtract the fraction of cheesecakes from this total.

Perform the subtraction: The difference between 3/4 (the total fraction of the two types of cakes) and 2/5 (the fraction of cheesecakes) gives you the fraction of carrot cakes.

The calculation for the difference in fractions can be done by finding a common denominator, which would be 20 in this case. The calculation would be as follows:

Convert fractions to have the same denominator: (3/4 × 5/5) - (2/5 × 4/4) = (15/20) - (8/20)

Subtract the fractions: 15/20 - 8/20 = 7/20

Therefore, the fraction of all cakes that are carrot cakes is 7/20.