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
$3,600

Answer 1

Let profit P(n) = mn + b. From P(25)=2000 and P(11)=600,

m = (2000−600)/(25−11) = 1400/14 = 100.

So P(n) = 100n + b. Use P(11)=600: 1100 + b = 600 ⇒ b = −500.

Thus P(36) = 100(36) − 500 = 3600 − 500 = $3,100.