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You are in charge of purchasing breakfast for an upcoming service activity involving about 50 people.

You have the choice to pick one of the following food items:

donuts ($0.30/each)
muffins ($0.50/each)
bagels ($0.40/each)
You have the choice to pick one of the following drinks:

individual cartons of milk or chocolate milk ($0.50/each)
individual bottles of orange juice or apple juice ($0.75/each)
You must stay within a budget of $100.

Write the following in your notebook.

What food item did you choose? What drink did you choose? Why?
Write an inequality to represent the cost of the items (less than or equal to $100) in standard form. Use x to represent the number of food items and y to represent the number of drinks.
Solve the inequality for y (slope-intercept form). Interpret the slope in context of the drinks and food items that are being purchased.
Graph the inequality and describe your graph and the process you used; for example, is your line dotted, solid, or shaded up or down? What does the shaded region represent?
What are the x and y-intercepts? Explain what these would represent in this situation.
What are the domain and range in this problem? Explain why you would or would not use the minimum and maximum values of the domain and range. How are the domain and range in the context of this problem different from the domain and range of any linear equation? What are the limits?

Respuesta :

MrRoyal

The limits of the domain and the range are 0 to 200, respectively; and you would use the minimum and maximum values of the domain and range because the graph of the inequality uses a solid line.

The items chosen

The items selected here could be any of the listed drinks and food items.

To solve this question, we use the following selection:

  • Muffins ($0.50/each) -- x
  • individual cartons of milk or chocolate milk ($0.50/each) -- y
  • Budget of $100

The inequality of the cost of items

In this case, we use the less than or equal to inequality.

So, we have:

0.5x + 0.5y ≤ 100

Solve the inequality for y (slope-intercept form).

In (b), we have:

0.5x + 0.5y ≤ 100

Subtract 0.5x from both sides

0.5y ≤ -0.5x + 100

Divide through by 0.5

y ≤ -x + 200

This means that the slope is -1, and it means that for every food item bought, there is a decrement of 1 in the drink.

The graph of the inequality

See attachment for the graph of the inequality

The features of the graph include

  • Straight and solid line
  • It is shaded down
  • The shaded region represents the acceptable solutions

What are the x and y-intercepts?

From the attached graph, we have:

  • x-intercept = 200
  • y-intercept = 200

This means that you can buy 200 food items, when you buy no drinks or buy 200 drinks when you buy no food item

What are the domain and range in this problem?

These are the acceptable x and y values of the graph.

From the attached graph, we have:

  • Domain: 0 ≤ x ≤ 200
  • Range: 0 ≤ y ≤ 200

The domain and range are different from the domain and range of any linear equation because the domain and the range of a linear equation is the set of all real numbers, while this domain and range are limited to 0 to 200

Read more about linear inequality at:

https://brainly.com/question/371134

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