Question

Suppose you start a business assembling and selling motorized scooters. It costs you $1500 for tools and equipment to get started, and the materials cost $200 for each scooter. Your scooters sell for $300 each.

a. Write and solve a system of equations representing the total costs and revenue of your business.
b. Describe what the solution means in terms of the situation.
c. Give an example of a reasonable number of scooters you could assemble and sell in order to make a profit, and find the profit you would make for that number of scooters.

Answer 1

Alright, so the money you make is automatically -1500 for the tools, so it's -1500. Next, the materials cost 200 dollars for each scooter, s, so we have -1500-200s. After that, we have 300 dollars for the sale of each scooter, so we have -1500-200s+300s. Adding -200 and 300 together, we have -1500+100s. To make a profit, that means 100s -1500 > 0. Dividing by 100, we have
s -15 >0  and s>15, so if you sold 16 scooters you'd make a profit. That profit would be 100*16-1500=1600-1500=100 dollars