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susan is arranging coffee mugs on shelves in her shop. she wanta each shelf to have the same number of mugs.she only wants one color of mug on each shelf. if she has 49 blue and 56 red mugs, what is the greatest amount vshe can put one each shelf ? how many shelves does she need for each color?

Respuesta :

The correct answers are:

7 mugs on each shelf; and 7 shelves for blue and 8 shelves for red.

Explanation:

To find the number of mugs that will fit on each shelf, we find the GCF (greatest common factor) of 49 and 56.  To do this, we find the prime factorization of each:

49 = 7(7)

56 = 7(8)

8 = 2(4)

4 = 2(2)

56 = 2(2)(2)(7)

The only common factor is 7, so this is the GCF.  This means that she needs to put 7 mugs on each shelf.

Since there are 49 blue mugs, she needs 49/7 = 7 shelves for them.

Since there are 56 red mugs, she needs 56/7 = 8 shelves for them.

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