Superlesson
Project 3-1
Advanced Algebra
Chapter 3, Solving Systems of Linear Equations and Inequalities
With the continuing growth of the Internet, more and more Internet Service Providers (ISPs) are springing into existence. If there's a service you're interested in, you may be able to decide which ISP offers a better deal by solving a system of equations.
Part A, Solving Systems of Equations Graphically
1. Find the fees charged by two ISPs that provide Internet access -- Sonic.net and dock.net.
a. Write an equation for the total cost of each service. Let y = the total cost and let x = the number of months. You may ignore JetLink's 2 month minimum.
b. Graph the two equations.
c. When will the cost of service from Zap be less than the cost of the service from JetLink?
d. When will the cost of service from JetLink be less than the cost of the service from Zap?
e. When will the cost of the two services be the same?
Part B, Solving Systems of Equations Symbolically
2. Some Internet providers give their customers a choice between paying more for more access and paying less for measured usage. Find the fees for dialup services charged by Idiom Consulting.
a. Write an equation that expresses the total cost c of an "Unlimited" account for the first month of use for h hours of use in excess of 240 hours. Include the setup charge and the monthly charge but no additional fees.
b. Write an equation that expresses the total cost c of an "Full" account for the first month of use for h hours of use in excess of 240 hours. Include the setup charge and the monthly charge but no additional fees.
c. Solve the system of equations you have written.
d. During the first month, how many hours in excess of 240 hours would you have to use Idiom's dialup modem service in order for a "Full" account to be cheaper than an "Unlimited" account.
e. Suppose you decided to pay for one extra connection. Write new equations for the total cost c of the first month of "Unlimited" and "Full" accounts for h hours of use. Assume you use the service for less than 240 hours.
f. During the first month, with one extra connection and less than 240 hours of use, how many hours would you have to use Idiom's dialup modem service in order for a "Full" account to be cheaper than an "Unlimited" account?
Part E, Making Connections
3. Telephone companies generally also give two options for service -- flat rate and measured rate. Find out one company's rate for flat rate and measured rate services.
a. Assume that measured-rate calls are charged at the rate of 5¢ per minute. What is the maximum amount of time that a measured-rate service can be used in one month without exceeding the cost of flat-rate service? (Remember that measured rate provides $3 worth of calls at no charge.)
b. Find the answer to 3a, assuming that measured-rate calls are charged at the rate of 15¢ per minute.
c. Find the answer to 3a, assuming that measured-rate calls are charged at the rate of 25¢ per minute?
d. Are you more likely or less likely to use the measured rate service as the price per minute rises? Explain.