Question

Hillary babysits for $6 per hour. She also works as a math tutor for $8 per hour. Her parents only allow her to work 14 hours per week. She wants to make at least $90. Write and graph a system of inequalities to represent this situation where x = babysitting and y = tutoring . Which represents a viable solution for hours worked by Hillary?

Answer 1

The answer would be:

(4.5, 8.5)

Answer 2

Here, x represents the number of hours of babysitting and y represents the number of hours of tutoring tutoring,

∵ babysitting costs $6 per hour and tutoring costs $8 per hour.

So, total earning = 6x + 8y

And, total hours = x + y

According to the question,

x + y ≤ 14 -----(1)

6x + 8y ≥ 90 ----(2)

Which is the required system of inequalities,

Relative equation of inequality (1) is x + y = 14, and inequality (2) is 6x + 8y = 90

Equation x + y = 14 having x-intercept = (14,0) and y-intercept = (0, 14)

While, equation 6x + 8y = 90 having x-intercept = (15,0) and y-intercept = (0,11.25)

≤ or ≥ shows solid line,

0 + 0 ≤ 14 ( true )

So, x + y ≤ 14 will contain the origin,

While, 6(0) + 8(0) ≥ 90 ( false )

So, the 6x + 8y ≥ 90 will not contain the origin.

Thus, the solution is the feasible region of the above system of inequalities.