Question

1 1. You can work at most 20 hours next week. You need to earn at least $92 to cover you weekly expenses. Your dog- walking job pays $7.50 per hour and your job as a car wash attendant pays $6 per hour. Write a system of linear inequalities to model the situation. 2. Marsha is buying plants and soil for her garden. The soil cost $4 per bag, and the plants cost $10 each. She wants to buy at least 5 plants and can spend no more than $100. Write a system of linear inequalities to model the situation.

Answer 1

Let x be the number of hours spent in dog-walking Let y be the number of hours spend in car washing. The maximum number of hours at work in a week is 20. Therefore x + y <=20 Salary for dog-walking job =$7.50/ hour Salary for car washing job=$6/ hour Total salary in a week earned through dog-walking job =7.50x Total salary in a week earned through car washing job=6y Least amount to be earned in a week =$92 Therefore, 7.50x +6y>=92 The required inequalities are x+y<=20; 7.50x+6y>=92 2. Let x be the number of soil bags Let y be the number of plants Cost per soil bag = $4 Cost per plant =$10 Minimum number of plants she wants to buy =5 Therefore, y>=5 Maximum amount she can spent =$100 Therefore 4x+10y<=100 The required inequalities are y>=5; 4x+10y<=100