An economy consists of three workers: Sam, Andrew, and Darnell. Each works 10 hours a day and can produce two services: mowing lawns and washing cars. In an hour, Sam can either mow 1 lawn or wash 1 car; Andrew can either mow 1 lawn or wash 2 cars; and Darnell can either mow 2 lawns or wash 1 car. For each of the scenarios listed, determine how many lawns will be mowed and how many cars will be washed per day and enter these values into the corresponding row.

a. All three spend all their time mowing lawns.

b. All three spend all their time washing cars.

c. All three spend half their time on each activity.

d. Sam spends half his time on each activity, while Andrew only washes cars and Darnell only mows lawns.

40 lawns would be mown , 0 cars would be washed

40 cars, 0 lawns

20 lawns 20 cars

25 lawns 25 cars

Explanation:

a. If they all mow lawns and they have 10 hours a day to work, the total number of lawn mown = (1 x 10) + (1 x 10) +(2 x 10) = 40 lawns

If they mow lawns only, they would wash cars. So, the  total of cars washed would be 0

b. If they all wash cars and they have 10 hours a day to work, the total number of cars washed = (1 x 10) + (2 x 10) +(1 x 10) = 40 cars

If they wash cars only, they would not mow any lawn. So, the  total of lawns mown would be 0

c If they all  spend half their time on each activity, they would wash cars for 5 hours and mow lawns for 5 hours

Lawns mown = (1 x 5) + (1 x 5) +(2 x 5) = 20 lawns

Cars washed = (1 x 5) + (2 x 5) +(1 x 5) = 20 cars

d. If Sam spends half his time on each activity, he would spend 5 hours on each activity. He would wash 5 cars and mow 5 lawns

If Andrew washes only cars, he would wash (2 x 10) = 20 cars

If Darnell only mows lawns, she would wash (2 x 10) = 20 lawns

This gives a total of 25 cars and 25 lawns

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