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

Answer 1

Let profit P(n) = mn + b. Slope m = (2000 − 600)/(25 − 11) = 1400/14 = 100.
Then b = 600 − 100(11) = −500. So P(n) = 100n − 500. For 36 lawns: P(36) = 100(36) − 500 = 3100.

Answer: $3,100.