34. The Pool Fun Company has learnedthat by pricing the newly released Fun Noodl

Question

34.     The Pool Fun Company has learnedthat by pricing the newly released Fun Noodle at $3, sales willreach 10,000 Fun Noodles per day during the summer. Raisingthe price to $5 will cause the sales to fall to 8,000 Fun Noodlesper day. Assume the relationship between price and number ofFun Noodles sold is linear.

a.                 Write an equation relating number of Fun Noodles sold toprice. Use ordered pairs of the form (price, number sold).

b.                Predict the number of Fun Noodles sold if the price is $3.50 perFun Noodle.

Explanation / Answer

Let us assume that number of fun noodles sold per day =y Price per noodle = x dollars (a) Now as per the question we know that y & x are relatedlinearly. So let the euqation be : y=m*x+c where m,c areconstants. Now in the first case x=3 and y=10000 Therefore the equationbecomes 10000=3*m+c (1) In the second case x=5 and y=8000 Therefore the equationbecomes 8000=5*m+c (2) Solving equation (1) and (2) simultaneously we get the value ofm=-1000 and c=13000 There the required equation isy=(-1000)x+13000 Ans (b)For the second part we know that price x=3.5 dollars There foresubstituting the value of x in the final equation we get y= (-1000)*(3.5) + 13000 y = 9500 Ans

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