Question

Jeff earns money mowing lawns. His earnings and hours worked represent a direct variation. He worked for 5 hours and earned $37.50. Determine the constant of proportionality (k) for dollars earned (d) per hours worked (h).

a) $7.50/hour
b) $10.00/hour
c) $5.00/hour
d) $6.25/hour

Answer 1

The constant of proportionality (k) for the amount Jeff earns mowing lawns, calculated by dividing his earnings by the hours worked, is $7.50 per hour.

Jeff earns money by mowing lawns and his earnings are directly proportional to the hours worked, which is a concept in linear equations with a constant of proportionality. To determine this constant (k), we divide his earnings by the number of hours worked. Jeff earned $37.50 for 5 hours of work, so k = $37.50 ÷ 5 hours = $7.50/hour. This means that for every hour Jeff works, he earns $7.50.

The correct answer to the question is option a) $7.50/hour, which is the constant rate of money he earns per hour of work.