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Edith babysits for x hours a week after school at a job that pays $4 an hour. She has accepted a
job that pays $8 an hour as a library assistant working y hours a week. She will work both jobs.
She is able to work no more than 15 hours a week, due to school commitments. Edith wants to
earn at least $80 a week, working a combination of both jobs.
Write a system of inequalities that can be used to represent the situation.
Graph these inequalities on the set of axes.
Determine and state one combination of hours that will allow Edith to earn at least $80 per week
while working no more than 15 hours.

Respuesta :

calculista

Answer:

Part A) The system of inequalities are

[tex]x+y\leq 15[/tex]

[tex]4x+8y\geq 80[/tex]

Part B) The graph in the attached figure

Part C) see the explanation

Step-by-step explanation:

Part A) Write a system of inequalities that can be used to represent the situation.

Let

x ----> the number of hours worked as a babysitter

y ----> the number of hours worked as a library assistant

we know that

She is able to work no more than 15 hours a week

so

[tex]x+y\leq 15[/tex] -----> inequality A

Edith wants to  earn at least $80 a week

The word "at least" means " greater than or equal to"

so

[tex]4x+8y\geq 80[/tex] ----> inequality B

Part B) Graph these inequalities on the set of axes.

Using a graphing tool

The solution of the system is the triangular shaded area in the attached figure

Part C) Determine and state one combination of hours that will allow Edith to earn at least $80 per week  while working no more than 15 hours

we know that

If a ordered pair is a solution of the system of inequalities, then the ordered pair must satisfy both inequalities. (The ordered pair lie in the shaded area of the solution set)

Looking at the graph

The ordered pair (4,9) lie in the shaded area

Verify if the ordered pair satisfy both inequalities

Inequality A

[tex]4+9\leq 15[/tex]

[tex]13\leq 15[/tex] ---> is true

so

The ordered pair satisfy the inequality A

Inequality B

[tex]4(4)+8(9)\geq 80[/tex]

[tex]88\geq 80[/tex] --> is true

so

The ordered pair satisfy the inequality B

therefore

The ordered pair is a solution of the system

(4,9)

That means

The number of hours worked as a babysitter in a week is 4 and  the number of hours worked as a library assistant  in a week is 9

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Edith can babysit for 5 hours and then work for 10 hours as the library assistant in a week so as to earn at least $80 a week

Inequality

An inequality is an expression that shows the non equal comparison of two or more numbers and variables.

Let x represent the number of hours at the $4 job and y represent the number of hours at the $8 job, hence:

x + y ≤ 15   (1)

Also:

4x + 8y ≥ 80  (2)

Graphing the inequality, the solution is at:

(5, 10)

Edith can babysit for 5 hours and then work for 10 hours as the library assistant in a week so as to earn at least $80 a week

Find out more on Inequality at: https://brainly.com/question/24372553

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