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?
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a: 16>B-S
b. 100>14*b + 5*(17-B)
a: 16<B+S Where S is shop
b. 100<12*B + 10*(16-B) where B is the babysitting hours
c. She may not have to work sixteen hours to get 100 dollars. For instance, 10 hours Babysitting gets 100 dollars
a) The inequality to represent the number of hours Bailey can work is:
12x + 10y ≤ 100
where x represents the number of hours she babysits and y represents the number of hours she works at the ice cream shop.
To obtain this inequality, we need to consider that Bailey can work a maximum of 16 hours per week. Therefore, we can write the equation x + y ≤ 16, as the total number of hours worked should be less than or equal to 16.
Next, we need to consider that Bailey wants to make at least $100 per week. Since she earns $12 per hour babysitting and $10 per hour working at the ice cream shop, we can multiply the number of hours worked by their respective hourly rates and set it to be greater than or equal to $100. This gives us the inequality 12x + 10y ≥ 100.
Considering that Bailey cannot exceed 16 hours, it becomes 12x + 10y ≤ 100.
b) The inequality to represent the amounts of money Bailey can make working is:
12x + 10y ≥ 100.
We obtained this equation by considering that Bailey wants to make at least $100 per week. Therefore, we multiply the number of hours worked by their respective hourly rates and set it to be greater than or equal to $100.
c) Two possible combinations of hours Bailey could work are:
- x = 8 hours of babysitting and y = 4 hours at the ice cream shop
- x = 6 hours of babysitting and y = 5 hours at the ice cream shop
We can calculate these combinations by trial and error or by solving the inequalities algebraically. These combinations work because they satisfy both the constraints of working a maximum of 16 hours and making at least $100.