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tatyana61 [14]
3 years ago
9

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 t

han 12 hours a week. Write and graph a system of linear equations.

Mathematics
1 answer:
Stolb23 [73]3 years ago
8 0

System of inequalities:

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

Graph is shown below.

<h2>Explanation:</h2>

Let:

x: Number of hour Charlene makes babysitting

y: number of hour Charlene makes gardening

We can represents each statement using inequalities as follows:

<h3>First statement:</h3>

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

  • 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

<em>At least </em>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

<h3>Second statement:</h3>

<em>She can work no more than 12 hours a week. </em>

<em>No more </em>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..

<h2>Learn more:</h2>

Inequalities: brainly.com/question/12890742

#LearnWithBrainly

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