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"The price of a hot dog at a baseball game is a linear function with the number of hot dogs sold. Let x be the number of hot dogs sold, and the price, p, is: p = 20 -0.025x The revenue earned selling x hot dogs at a ball game and the cost for making x hot dogs at a ball game are given below. R(x) = 20x – 0.025x? and C(x) = 2x + 20 What is the price of a hot dog that will result in the baseball stadium making maximum profit?" A student attempts to solve this question by doing the following: P(x) = R(x) – C(x) = 20x – 0.025x² – (2x +20) P(x) = - 20+ 18x – 0.025x? 18 X = - a (-0.025) = 720 The number of hot dogs that maximizes profit is 720, and the price that results in 720 hot dogs sold is: p = 20 - 0.025(720) = 2 $2 dollars will result in maximum profit. What did the student do wrong? What can they do to fix it?

"The price of a hot dog at a baseball game is a linear function with the number of hot dogs sold. Let x be the number of hot dogs sold, and the price, p, is: p = 20 -0.025x The revenue earned selling x hot dogs at a ball game and the cost for making x hot dogs at a ball game are given below. R(x) = 20x – 0.025x? and C(x) = 2x + 20 What is the price of a hot dog that will result in the baseball stadium making maximum profit?" A student attempts to solve this question by doing the following: P(x) = R(x) – C(x) = 20x – 0.025x² – (2x +20) P(x) = - 20+ 18x – 0.025x? 18 X = - a (-0.025) = 720 The number of hot dogs that maximizes profit is 720, and the price that results in 720 hot dogs sold is: p = 20 - 0.025(720) = 2 $2 dollars will result in maximum profit. What did the student do wrong? What can they do to fix it?

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.3: Lines
Problem 60E
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"The price of a hot dog at a baseball game is a linear function with the number of hot dogs sold. Let x be the number of hot dogs sold, and the price, p, is: p= 20 -0.025x The revenue earned selling x hot dogs at a ball game and the cost for making x hot dogs at a ball game are given below. .2 R(x) = 20x – 0.025x C(x) = 2x +20 and What is the price of a hot dog that will result in the baseball stadium making maximum profit?" A student attempts to solve this question by doing the following: P(x) = R(x) – C(x)= 20x – 0.025x² – (2x +20) P(x) = - 20+ 18x – 0.025x2 18 X = = 720 a (-0.025) The number of hot dogs that maximizes profit is 720, and the price that results in 720 hot dogs sold is: p = 20 - 0.025(720) = 2 $2 dollars will result in maximum profit. What did the student do wrong? What can they do to fix it?
Transcribed Image Text:"The price of a hot dog at a baseball game is a linear function with the number of hot dogs sold. Let x be the number of hot dogs sold, and the price, p, is: p= 20 -0.025x The revenue earned selling x hot dogs at a ball game and the cost for making x hot dogs at a ball game are given below. .2 R(x) = 20x – 0.025x C(x) = 2x +20 and What is the price of a hot dog that will result in the baseball stadium making maximum profit?" A student attempts to solve this question by doing the following: P(x) = R(x) – C(x)= 20x – 0.025x² – (2x +20) P(x) = - 20+ 18x – 0.025x2 18 X = = 720 a (-0.025) The number of hot dogs that maximizes profit is 720, and the price that results in 720 hot dogs sold is: p = 20 - 0.025(720) = 2 $2 dollars will result in maximum profit. What did the student do wrong? What can they do to fix it?
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