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15) In a bakery, 3/4
of all the cakes are two types: cheesecake and carrot cake. The cheesecakes make 2/5
of all the cakes. What fraction of all the cakes are carrot cakes?

Sagot :

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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