Mathematics, 02.09.2019 14:30 cloudFF

Alandscaper 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?
$2,600
$2,880
$3,100
$3,600

Answers: 1

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Answer from: pippyysanchezz

The answer is $3,100.

Step-by-step explanation: Given that 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.We are to calculate the profit that he will receive in a week that he services 36 lawns

Let 'x' represents the number of laws the landscaper serviced in a week in which he makes a profit of '$y'.

So, when x = 25, y = 2000 and when x = 11, y = 600.

Thus, A(25, 2000) and B(11, 600) are two points on the linear function that will be a straight line.

The equation of the line AB will be

$y-600=\dfrac{2000-6000}{25-11}(x-11)\\\\\\\Rightarrow y-600=\dfrac{1400}{14}(x-11)\\\\\\\Rightarrow y-600=100(x-11)\\\\\Rightarrow 100x-y=500.$

Therefore, when he services 36 lawns, then x = 36. So,

$100\times 36-y=500\\\\\Rightarrow y=3600-500\\\\\Rightarrow y=3100.$

Thus, the answer is (c) $3,100.

Answer from: Arinola

Hello there!

We know that the landscaper makes $2000 of profit when he services 25 lawns, and he makes $600 in profit when he services 11 lawns.

We also know that the relation between the profit and the number of lawns serviced is a linear relation, this means that the profit is of the form:

P(L) = K*L + b

where K is the slope, L is the number of lawns serviced and b is the y-intercept

Let's find the value of the slope, if we have two points (x1,y1) and (x2,y2)

the slope between them is: $a = \frac{y2 - y1}{x2 - x1}$

in our case, the points are: (25, 2000) and (11, 600)

then the slope is:

$k = \frac{2000 - 600}{25 - 11} = \frac{1400}{14}=100$

now we have the function profit as:

P(L) = 100L + b

let's find the value of b.

we know that P(11) = 600 = 100*11 + b = 1100 + b

then b = 600 - 1100 = 500

and our profit function is:

P(L) = 100L - 500

now, if L = 36, we need to see

P(36) = 100*36 - 500 = 3100

this means that if he service 36 lawns, he makes $3100, then the right answer is the third one.

Answer from: Quest

clock

step-by-step explanation:

Answer from: Quest

you never say the total so we cant find the percentage used for petrol

step-by-step explanation:

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