Question

A landscaper makes a $2,000 profit in a week when he services 25 lawns. He makes a $600 profit in a week when he services 11 lawns. If his profit for the week is a linear function of the number of lawns serviced, how much profit would he receive in a week that he services 36 lawns?

Answer 1

He will earn $3,600. but $3,600 - that -800 will equal $2600 profit

Answer 2

Profit = $3100

Explanation:

Since it is a LINEAR FUNCTION, we can take laws as the x-coordinate and profit as y-coordinate. Thus we have 2 points that we can write:

Point 1: (25,2000)

Point 2: (11, 600)

With two points, we can find equation of the line passing through this two points by the equation:

`y-y_1=(y_2-y_1)/(x_2-x_1)(x-x_1)`

Where
`(x_1,y_1)=(25,2000)` and
`(x_2,y_2)=(11,600)`

Substituting the values, we have:

`y-y_1=(y_2-y_1)/(x_2-x_1)(x-x_1)\\y-2000=(600-2000)/(11-25)(x-25)\\y-2000=(-1400)/(-14)(x-25)\\y-2000=100(x-25)\\y=100x-100(25)+2000\\y=100x-2500+2000\\y=100x-500`

We need to find profit when 36 laws are services. Since x is laws, and y is profit, we plug in 36 into x and solve for y:

`y=100x-500\\y=100(36)-500\\y=3100`

Profit is $3100