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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?

Respuesta :

augustalston91
He will earn $3,600. but $3,600 - that -800 will equal $2600 profit
TaeKwonDoIsDead

Answer:

Profit = $3100


Step-by-step 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:

[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]

Where [tex](x_1,y_1)=(25,2000)[/tex] and  [tex](x_2,y_2)=(11,600)[/tex]


Substituting the values, we have:

[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)\\y-2000=\frac{600-2000}{11-25}(x-25)\\y-2000=\frac{-1400}{-14}(x-25)\\y-2000=100(x-25)\\y=100x-100(25)+2000\\y=100x-2500+2000\\y=100x-500[/tex]


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:

[tex]y=100x-500\\y=100(36)-500\\y=3100[/tex]

Profit is $3100

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