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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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