Question

Ezra works two summer jobs to save for a laptop that costs at least $1100 he charges $15/hr to mow lawns and $10 an hour to walk dogs. Recall the inequality that represents this situation: 15x + 10y >_ 110

is (60,20) a solution? How do you know? What does this power represent?

Answer 1

The inequality that represents this situation is 15x + 10y ≥ 1100, since Ezra needs to earn at least $1100 to buy the laptop.

To check if (60, 20) is a solution to this inequality, we need to substitute x = 60 and y = 20 into the inequality and see if it is true:

15(60) + 10(20) ≥ 1100

900 + 200 ≥ 1100

1100 ≥ 1100

Since 1100 ≥ 1100 is true, this means that (60, 20) is a solution to the inequality. This means that if Ezra works 60 hours mowing lawns and 20 hours walking dogs, he will earn enough money to buy the laptop.

The point (60, 20) represents the combination of hours worked for mowing lawns (x) and walking dogs (y) that will result in Ezra earning enough money to buy the laptop. The x and y values are the inputs or variables, while the inequality 15x + 10y ≥ 1100 is the constraint that must be satisfied. The solution (60, 20) is the output or result of the system of inequalities, and represents the combination of hours worked that will satisfy the constraint.