Emma and her children went into a restaurant where they sell hotdogs for $4 each and drinks for $1.50 each. Emma has $30 to spend and must buy no less than 9 hotdogs and drinks altogether. If xx represents the number of hotdogs purchased and yy represents the number of drinks purchased, write and solve a system of inequalities graphically and determine one possible solution.

Answer:

6 hotdogs and 4 drinks

Step-by-step explanation:

4x + 1.50y = 30

For questions like this, you can do the equation that represents the price of the products first.

x + y  [tex]\geq[/tex] 9

After that, you can write the equation that represents the quantities.

Now, you just have to graph it to find the solution. When you're graphing, make sure that y is alone on one side. Here's how you rearrange the equations:

The first equation:

4x + 1.50y =30

*Subtract 4x from both sides, which leads to:

1.50 y = -4x + 30

*Divide by 1.50 on both sides, which leads to:

y = -2.66x + 20

The second equation:

x + y  [tex]\geq[/tex] 9

*Subtract x from both sides, which leads to:

y  [tex]\geq[/tex] -1x + 9

Now, use any graphing calculator (I prefer Desmos) to graph these two equations. In fact, you can just graph it on paper, too.

Here is the graph: (it is attached as a file)

You can look for any points that are on the red line but are also shaded blue. Make sure you look only in Quadrant 1- don't go into the negatives! One good point to choose would be (6,4)- this means that you buy 6 hotdogs and 4 drinks.

Answer:

[tex]y\geq 9-x[/tex] shaded up

[tex]y\leq 20-\frac{8}{3} x\\[/tex] shaded down

4 hotdogs, 8 drinks

Step-by-step explanation:

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