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Holly had a total of 150 books and magazines. She bought another 50 books and gave away 1/3 of her magazines. The number of books and magazines became the same. What was the ratio of the number of books to the number of magazines at first? (Give your answer in the simplest form.)

 Sep 20, 2021
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B  =  original number of books.

M  =  original number.

 

B + M  =  150

(B + 50) + (M - 1/3M  =  150     --->     B + 50  +  2/3M  =  150     --->     B + 2/3M  =  100

 

Combining:     B +      M  =  150

                       B + 2/3M  =  100

 

Subtracting:          1/3M  =  50     --->     M  =  150

 

She starts with 150 magazines, so she starts with 0 books.

 

The ratio of the number of books to the number of magazines is:  0 / 150  =  0.

 Dec 6, 2021

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