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Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.Russell wrote a business plan for an entrepreneurship class, and now he has to make bound copies. Russell could use a printer who charges a setup fee of and for every copy printed. Another possibility is to go to the office supply store, where he could pay an up-front fee of and per copy. There is a certain number of copies that makes the two options equivalent in terms of cost. How many copies is that? How much would the copies cost?For copies, the cost is .
Full solution
Q. Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.Russell wrote a business plan for an entrepreneurship class, and now he has to make bound copies. Russell could use a printer who charges a setup fee of and for every copy printed. Another possibility is to go to the office supply store, where he could pay an up-front fee of and per copy. There is a certain number of copies that makes the two options equivalent in terms of cost. How many copies is that? How much would the copies cost?For copies, the cost is .
- Define Variables: Step : Let's define the variables.Let be the number of copies Russell needs to print.Let be the total cost for printing copies.
- Cost Equation for Printer: Step : Write the equation for the cost of using the printer.The printer charges a setup fee of and for every copy.So the cost equation for the printer is: .
- Cost Equation for Office Supply Store: Step : Write the equation for the cost of using the office supply store.The office supply store charges an up-front fee of and per copy.So the cost equation for the office supply store is: .
- Set Equations Equal: Step : Set the two equations equal to each other to find the number of copies where the costs are equivalent.
- Solve for x: Step : Solve for x by isolating the variable.
- Substitute for Total Cost: Step : Substitute the value of back into either of the original equations to find the total cost . Using the printer's cost equation:
- Verify Solution: Step : Verify the solution by substituting into the office supply store's cost equation.Using the office supply store's cost equation:
