System of inequalities:
[tex](1) \ 10x+5y\geq 80 \\ \\ (2) \ x+y\leq 12[/tex]
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:
[tex]10x[/tex]
- The amount of money she makes gardening is:
[tex]5y[/tex]
- 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:
[tex]a\geq b[/tex]
Then, in this context:
[tex]10x+5y\geq 80[/tex]
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:
[tex]a\leq b[/tex]
So:
[tex]x+y\leq b[/tex]
So, our system of inequalities would be:
[tex](1) \ 10x+5y\geq 80 \\ \\ (2) \ x+y\leq 12[/tex]
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: https://brainly.com/question/12890742
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