a) Let x represent the number of shirts bought.
For our company:
Total cost = 5 + 10x
For the other company:
Total cost = 20 + 7x
b) If the customer wants to buy 3 shirts:
For our company: Total cost = 5 + 10*3 = $35
For the other company: Total cost = 20 + 7*3 = $41
Therefore, the customer should buy from our company if they want to buy 3 shirts.
If the customer wants to buy 10 shirts:
For our company: Total cost = 5 + 10*10 = $105
For the other company: Total cost = 20 + 7*10 = $90
Therefore, the customer should buy from the other company if they want to buy 10 shirts.
c) To solve the system of equations:
5 + 10x = 20 + 7x
Subtract 7x from both sides:
3x = 15
x = 5
This means that if the customer buys 5 shirts, it would cost the same amount from both companies. Additionally, if they buy fewer than 5 shirts, it's cheaper to buy from our company, and if they buy more than 5 shirts, it's cheaper to buy from the other 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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