Question
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.
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.
Answers
GPT 3.5
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.
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.