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1986 AJHSME Problems/Problem 16

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Problem

A bar graph shows the number of hamburgers sold by a fast food chain each season. However, the bar indicating the number sold during the winter is covered by a smudge. If exactly 25\% of the chain's hamburgers are sold in the fall, how many million hamburgers are sold in the winter?

size(250);void bargraph(real X, real Y, real ymin, real ymax, real ystep, real tickwidth, string yformat, Label LX, Label LY,...

\text{(A)}\ 2.5 \qquad \text{(B)}\ 3 \qquad \text{(C)}\ 3.5 \qquad \text{(D)}\ 4 \qquad \text{(E)}\ 4.5

Solution

What we want to find is the number of hamburgers sold in the winter. Since we don't know what it is, let's call it x. From the graph, we know that in Spring, 4.5 million hamburgers were sold, in the Summer was 5 million and in the Fall was 4 million. We know that the number of hamburgers sold in Fall is exactly \frac{1}{4} of the total number of hamburgers sold, so we can say that...

4 \times \text{Fall} = \text{Spring} + \text{Winter} + \text{Fall} + \text{Summer}

4 \times 4 = 4.5 + 4 + x + 5

16 = x + 13.5

2.5 = x

The answer is 2.5, or \boxed{\text{A}}

See Also

1986 AJHSME (ProblemsResources)
Preceded by
Problem 15
Followed by
Problem 17
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Looking for a challenging geometry text? Preparing for MATHCOUNTS or the AMC exams? Check out Art of Problem Solving's Introduction to Geometry by Richard Rusczyk.
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