Question

Charlene makes $10 per hour babysitting and $5 per hour gardening. She wants to make at least $80 a week, but can work no more than 12 hours a week. Write and graph a system of linear equations.

Answer 1

System of inequalities:

$(1) \ 10x+5y\geq 80 \\ \\ (2) \ x+y\leq 12$

Graph is shown below.

Explanation:

Let:

x: Number of hour Charlene makes babysitting

y: number of hour Charlene makes gardening

We can represents each statement using inequalities as follows:

First statement:

Charlene makes $10 per hour babysitting and $5 per hour gardening. She wants to make at least $80 a week,

• The amount of money she makes babysitting is:

$10x$

• The amount of money she makes gardening is:

$5y$

• She wants to make at least $80 a week

At least in this context means that the minimum amount of money she can makes is $80. In other words, if a is at least b we write:

$a\geq b$

Then, in this context:

$10x+5y\geq 80$

Second statement:

She can work no more than 12 hours a week.

No more in this context means that the maximum numbers of hours she can work in a week is 12. In other words, if a no more than b we write:

$a\leq b$

So:

$x+y\leq b$

So, our system of inequalities would be:

$(1) \ 10x+5y\geq 80 \\ \\ (2) \ x+y\leq 12$

By using graphing tool, we get the graph below. The solution is that where both the region of the first and second inequality overlap. Keep in mind that the symbols ≥ ≤ tells us that $80 and 12 hours respectively are included in our solution..

Learn more:

Inequalities: brainly.com/question/12890742

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