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Question 484152: I need to solve the story problem:
A man's shoe size 7 1/2= 10inches, and a 11 1/2= 11 inches. I have to write a linear equations and figure out what a 9 1/2 equals.
Answer by chessace(471)   (Show Source):
You can put this solution on YOUR website! Of course there is the implied assumption that shoes sizes are linear.
Using the standard y = f(x), x is the shoe size because in the end you are given one such. y is the length in inches.
Given f(7.5) = 10 and f(11.5) = 11, we see that an increase in x of 4 results in an increase in y of 1. So the slope of the linear function is 0.25.
One could find f(0) but it would be weird in the shoe store.
So define z = x - 7.5, and w = y - 10.
This does not change the slope.
w = g(z) = 0.25 z
g(9.5 - 7.5) = 0.25 * 2 = 0.5
f(9.5) = 0.5 + 10 = 10.5
Reasonable check: the asked for 9.5 is half way between the given limits, and the "10 1/2" answer is half way between the function limits, so that is linear.
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