Write an inequality to represent the cost of the items in standard form. Use x to represent the number of food items and y to represent the number of drinks

Question

You have the choice to pick one of the following food items: •donuts ($0.30)

•muffins($0.50)

•bagels($0.40)

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)

you must stay within a budget of $100

write an inequality to repaint the cost of the items in standard form.use x to represent the number of food items and y to represent the number of drinks.

Answer 1

In general, the cost of the food and drinks you buy must be $100 or less. If a food item costs $0.50 and you buy 5 of them, then your cost is ($0.50)(5) = $2.50. So the general formula is:

(cost of a food item)·(number of food items bought) + (cost a drink item)·(number of drink items bought) ≤ $100

You can choose whichever food and drink items you want from the above choices. There are multiple possible combinations, but you only need to choose one. Use the actual cost of the food and drink items you choose and use x and y for the number of food and drink items bought.

Answer 2

Standard linear form is Ax + By = C

For this example, I will pick muffins as my food item and apple juice as my drink choice. The instructions say to use x to represent the number of food items (so muffins) and y to represent the number of drinks (so apple juice).

A is the coefficient representing the cost of each muffin($0.50) and x is the quantity of number of muffins purchased. Thus Ax or $0.50x represents the cost of the x number of muffins. 2 muffins will thus cost $0.50 x 2 or $1.00 and 10 muffins will cost $0.50 x 10 or $5.00.

B is the coefficient representing the cost of each apple juice ($0.75) and y is the quantity of number of apple juices purchased. Thus By or $0.75y represents the cost of the y number of apple juices. 2 cartons of apple juice will thus cost $0.75 x 2 or $1.50 and 10 apple juice will cost $0.75 x 10 or $7.50.

We can use the equation $0.50x + $0.75 y = $100 to find the number of muffins and apple juices we can purchase to add up to $100 dollars. There are many options( any coordinate on this line https://www.desmos.com/calculator/xnhvyubz8m) as to combinations of apple juice/muffins numbers you can combine to get the $100. Because (107, 62) and (200, 0) are on the line, two examples might be 107 muffins and 62 apple juices or 200 muffins and 0 apple juices.

Because the question is asking for an inequality we need to use the greater than > or less than sign instead of the= sign. Which do you think is appropriate if we want the cost of our apple juice and muffins to be within the budget of $100? (Do you think that means less than or more than $100?)

Hope this helps or at least can be a good starting point!