Question

A school library spends $80 a month on magazines. The average price for magazines bought in January was 70 cents more than the average price in December. Because of the price increase, the school library was forced to subscribe to 7 fewer magazines. How many magazines did the school library subscribe to in December?

Answer 1

Answer:

  32 magazines

Step-by-step explanation:

If x is the number of subscriptions in December, then the number in January is x-7.

The relationship between the average price of magazines in the two months is ...

  80/(x-7) -80/(x) = 0.70 . . . . . . . . .Jan price - Dec price = 0.70

  80(x) -80(x -7) = 0.70(x)(x-7) . . . . multiply by the denominators

  0.7x^2 -4.9x +560 = 0 . . . . . . . . put in standard form

  x^2 -7x +800 = 0 . . . . . . . . . . . . . divide by 0.7

  (x -32)(x +25) = 0 . . . . . . . . . . . . . factor

The product is zero when one of the factors is zero. x=32 or -25. The sensible solution for this problem is x=32.

The school library subscribed to 32 magazines in December.