Practice #9

Below are two practice problems. Solve one of them using the substitution method and one using the addition/subtraction method. You can choose which problem to solve using substitution, and which to solve using addition/subtraction.

  1. Salesmen at Northern Castings pay for supplies under one of two payment plans.

    Payment Plan Option I: $300 base salary per month and 6% commission on sales made. If x is the amount of sales, the amount of monthly pay earned, y, is given by the equation y I = 300 + 0.06x.  

    Payment Plan Option II: Base pay of $150 and then 10% commission on sales made. If x is the amount of  sales, the amount of monthly pay earned, y, is given by the equation yII = 150 + 0.10x.

    At what value of their sales, x, will the income for both options be the same, yI= yII.= y. So the two equations are:

    y = 300 + 0.06x  

    y = 150 + 0.10x  

     

  2. The Great American Treehouse is a place that holds parties. The base cost for a party is $69.96 for up to 15 people, then $3 for each additional person over 15 people. The cost of a party (in dollars) at The Great American Treehouse is given by the following equation, where y is the total cost, and x is the number of people attending the party.

    y = 69.96 + 3 (x – 15)

    If you wish to purchase ice cream for the party from Chunk’s Ice Cream Parlor, you can purchase unlimited amounts of ice cream at a cost of $3.96 per person. The cost of ice cream is given by the following equation, where y is the total cost and x is the number of persons.

    y = 3.96x

    Solve this system of equations, and find both the cost and number of people for whom the cost of ice cream will be equal to the cost of using The Great American Treehouse.

    Solution
    [Solution to Practice]