Video: Forming and Solving Simultaneous Equations in a Real-World Context

Video Transcript

Anthony finds two plumbers online: the first charges twenty dollars per hour of labor, while the second charges a fixed charge of forty dollars per job plus an hourly labor charge of fifteen dollars. After how many hours will the second plumber be cheaper than the first?

So we wanna know when will the second plumber cost less than the first plumber. The second plumber charged a fixed amount of forty dollars plus an hourly charge of fifteen, so fifteen times the number of hours that they worked. And then the first plumber was twenty dollars per hour, so twenty times 𝑥, where 𝑥 represents the number of hours.

So when will forty plus fifteen 𝑥 be less than twenty 𝑥? We need to solve for 𝑥. If we subtract fifteen 𝑥 from both sides, we have forty is less than five 𝑥. We need to divide both sides by five now. So we have eight is less than 𝑥. It’s usually read with the variable on the left, so notice the bigger end opens to the 𝑥.

When we flip that around, the bigger end of the inequality needs to open to the 𝑥. So 𝑥 is greater than eight. So this means the second plumber won’t be cheaper than the first until after eight hours. So if the job would require more than eight hours, the second plumber would be cheaper.