Question

Think about the process a machine can make 56 parts in 4 hours. It can also make in ______. Which rates could you use to write an equation of the form y = kx that represents the number of parts y the machine can make in ______? What is that equation?

Answer 1

The equation representing the number of parts a machine can produce in x hours is y = 14x, with the rate of production being 14 parts per hour.

Step-by-step explanation:

The question is about determining the rate at which a machine produces parts and writing an equation to model this relationship. The machine can make 56 parts in 4 hours. To find the rate of parts made per hour (k), we divide the total parts made by the total hours: k = 56 parts / 4 hours = 14 parts per hour. So, the equation of the form y = kx that represents the number of parts y the machine can make in x hours is y = 14x.

The concept discussed here relates to labor productivity and the production possibilities that change with improvements in resources and technology, such as using calculators and computers. When labor productivity increases, the total product (TP) or output (Q) is affected. This concept is similar to the examples provided where labor and capital are utilized to maximize production, whether it's cutting down trees or manufacturing goods.