a) Let x represent the number of shirts bought.
For the first company:
Total cost = 5 + 10x
For the second company:
Total cost = 20 + 7x
b)
For 3 shirts:
First company: Total cost = 5 + 10(3) = $35
Second company: Total cost = 20 + 7(3) = $41
For 10 shirts:
First company: Total cost = 5 + 10(10) = $105
Second company: Total cost = 20 + 7(10) = $90
c) To solve the system of equations:
5 + 10x = 20 + 7x
3x = 15
x = 5
The solution x=5 means that if the customer buys 5 shirts, it will cost the same amount at both companies - $55. For any amount of shirts above 5, it is more cost-effective to buy from the first company; for any amount of shirts below 5, it is more cost-effective to buy from the second company.
There is a customer in another state who would like to buy some of your t-shirts. It will cost you a flat rate of $5 to ship to this customer. There is another company that sells the same t-shirts $7, but the shipping cost is $20.
a) Write two equations to represent the customer’s total cost based on how many shirts they buy from you or the other company.
b) If the customer wants to buy 3 shirts, from whom should they buy? What about 10 shirts? c) Solve this system of equations using any method you want. Explain what the solution means in terms of this situation.
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