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
Answered by
GPT 3.5
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.
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.