Question

The total cost of renovation depends on labor and materials. You decide to budget $25,000 towards labor. The amount, A, that each worker earns varies inversely to the number of workers on the job, n.

1) complete the table to indicate the amount earned for the given number of workers.

2) what do you notice about the product, A*n?

Answer 1

1. see attached
2. A*n is the constant 25000

Explanation:

1)

The amount A is said to vary inversely with n, so the equation relating the two is ...

A = k/n

The value of k can be found by multiplying this equation by n:

k = nA

Using values from the first line of the table, we find ...

k = (1)(25000) = 25000

So the relation we need to use to fill the table is ...

A = 25000/n

The filled table is attached.

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2)

As we saw in part 1, the product A*n is the constant of proportionality. It is a constant.