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There are 280 pices of fruit. There are twice as many raspberries as blueberries,three times as many grapes as cherries, and four times as many cherries as raspberries. How many cherries are there?

Answer :

Answer:

There are 64 cherries.

Step-by-step explanation:

We are given the following in the question:

Total number of pieces of fruit = 280

Let [tex]x[/tex] be the number of blueberries.

Number of raspberries =

[tex]=2\times \text{Number of blueberries}\\=2x[/tex]

Number of cherries =

[tex]4\times \text{Number of raspberries}\\=4\times 2x\\ = 8x[/tex]

Number of grapes =

[tex]3\times \text{Number of cherries}\\=3\times 8x\\=24x[/tex]

Thus, we can write the equation:

[tex]x + 2x + 8x + 24x = 280\\35x = 280\\x = 8[/tex]

Number of cherries =

[tex]8x = 8\times 8 = 64[/tex]

Thus, there are 64 cherries.

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