A local retailer has determined thatthe number x of PortaBoy game systems soldin a week is related to the price p in dollars ofeach system. 30 game systems were sold whenthe price was $105. When the systems went onsale the following week, 50 systems were soldat $75 a piece.(a) Find a linear function which fits this data.Use the weekly sales x as the independentvariable and the price p as the dependentvariable.Answer: p(x)=(b) Find a suitable applied domain:(c) If the retailer wants to sell 90 PortaBoys nextweek, what should the price be?Answer: p=dollars

Solution : A local retailer has determined that the number x of PortaBoy game systems sold in a…

Answered: A local retailer has determined that…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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2. A toy company finds there is a linear relationship between p, the price they charge for a playground ball, and n(p), the number of balls they sell during a year. When they charge $3, they sell 8000 balls during the year. However, sales drop to 5200 balls when they charge $5 each. a. Write an equation for the linear function n(p). b. Use your function to determine the number of balls they can expect to sell during the year if they charge $6.50 for a ball.
What equation would I set this word problem up as?
A minivan was purchased for $32,000. If the value of the minivan depreciates by $1,700 per year, find a linear function that models the value V of the car after t years. Use the function and find the value of the car after 5 years. (A) V(t) = -1,700t + 32,000; value after 5 years = $23,500 B V(t) = -1,700 + 32,000; value after 5 years = $30,300 (C) V(t) = 1,700 + 32,000; value after 5 years = $33,700 D V(t) = 1,700t + 32,000; value after 5 years = $40,500
Find a linear cost function. Thirty units cost $1500; 120 units cost $5640.
A company that makes sweatshirts is willing to supply 156 sweatshirts each month if the price is $24 each and will supply 204 sweatshirts each month if the price is $36 each. Find the linear supply function, qS where qS is the number of sweatshirts the company is willing to make available per month at a price of p dollars per sweatshirt. A. A. qS = 0.25p – 15 B. qS = 4p + 60 C. qS = 12p + 48 D. qS = p/12 – 48
Sunny Mountain Company will make 1970 snow blowers available when the unit price is $680. At a unit price of $850, they will market 5230 snow blowers. Find the equation relating the unit price of a snow blower to the quantity supplied if the relationship is known to be linear. p(x) How many snow blowers will be marketed when the unit price is $720? (round UP to an integer) = What is the lowest price at which a snow blower will be marketed? (round UP to a whole dollar) $
A baseball team plays in a stadium that holds 50000 spectators. With the ticket price at $8 the average attendance has been 21000. When the price dropped to $6, the average attendance rose to 25000. Assume that attendance is linearly related to ticket price. What ticket price would maximize revenue? s
A car initially sold for $23,999. Its class life is 12 years, and the car depreciates by $750 each year. Express this as a linear function. Find the salvage value. Then, find the value after six years.
The cost in dollars, y, to participate x days in a bike tour is a linear function. Lou’s bike tour is described by the equation y = 6x + 40. The cost of Mary’s bike tour is $120 for a 14-day bike tour. If both Lou and Mary take 14-day tours, whose bike tour costs less? *
A store is having a sale where all items are 16% off. Write an equation to represent the relationship between the sale price of an item, s, and the original price, p, where s and p are in dollars.
7. Sky Launch Trampoline Park charges Customers $9.50 per hour they spend jumping. Each customer must also pay $2.50 for grip socks. Write an equation in slope-intercept form to represent this linear function. Derrick spent $31 at Sky Launch Trampoline Park on Sunday. How many hours did he jump?
Suppose that the number of tee shirts sold (N) depends linearly on the price charged (x). Write an equation showing this dependence.

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