Question

Bailey babysits for $12 an hour. She also works at an ice cream shop for $10 an hour. Her parents say she is only allowed to work a maximum 16 hours a week so she can still concentrate on her schoolwork. She wants to make at least $100 a week.a) Write an inequality to represent the number of hours Bailey can work. Explain how you got that equation.b) Write an inequality to represent the amounts of money she can make working. Explain how you got that equation.c) Give TWO possible combinations of hours Bailey could work. How did you get these answers? Why do these combinations work?

Answer 1

Answer:

$x + y \leq 16$

$12x + 10y \geq 100$

c) 9 hours of babysitting and 6 hours in ice cream shop.

10 hours of babysitting and 5 hours in ice cream shop.

Step-by-step explanation:

We are given the following in the question:

Earning from babysitting = $12 an hour

Earning from ice-cream shop = $10 an hour

Let x be number of hours for babysitting in a week and y be the number of hours working in ice cream shop in a week

a) Bailey is only allowed to work a maximum 16 hours a week. Thus, the sum of hours in a week together from ice cream shop and babysitting should be less than equal to 16. Thus, the inequality to represent the number of hours Bailey can work can be written as

$x + y \leq 16$

b) Bailey wants to make at least $100 a week. Thus, the sum of total earning  from ice cream shop and babysitting should be greater than 100 dollars. Thus, the inequality to represent the total earning of Bailey can be written as

$12x + 10y \geq 100$

c) The attached image shows the graph for the two inequalities.

The black region shows the solution to inequality to represent the number of hours and red region represents the solution to inequality for the total earning of Bailey.

c) The common shaded region gives the solution to both the inequalities.

Any two possible combination for the possible combinations of hours Bailey could work from graph are:

(9,6), (10,5)

9 hours of babysitting and 6 hours in ice cream shop.

10 hours of babysitting and 5 hours in ice cream shop.