Under his household expense budget category, Mark has...

Under his household expense budget category, Mark has allocated $\$ 60$ per month for pet food. He can purchase wet food in a can for $\$ 1.50$ per can or dry food in a bag for $\$ 3$ per bag. a. Determine a budget line equation for this situation. b. Graph the budget line that will depict the different combinations of cans and bags that Mark can purchase while still remaining within his budget. c. Name a combination of bags and cans that will allow him to d. Name a combination of bags and cans that will keep him under budget. e. Name a combination of bags and cans that will cause him to be over budget.

Under his household expense budget category, Mark has allocated $\$ 60$ per month for pet food. He can purchase wet food in a can for $\$ 1.50$ per can or dry food in a bag for $\$ 3$ per bag.
a. Determine a budget line equation for this situation.
b. Graph the budget line that will depict the different combinations of cans and bags that Mark can purchase while still remaining within his budget.
c. Name a combination of bags and cans that will allow him to
d. Name a combination of bags and cans that will keep him under budget.
e. Name a combination of bags and cans that will cause him to be over budget.

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Key Concepts

Budget Constraint

A budget constraint represents the combinations of different goods or services that a consumer can purchase with a limited amount of money. It is expressed as an equation that sets the total expenditure equal to the available budget, illustrating the trade-offs between spending on different items.

Linear Equation

A linear equation, especially in the context of budgeting, is used to model the relationship between quantities of two different goods that can be purchased given a fixed budget. The equation typically shows how the cost of one good affects the maximum amount of the other good that can be bought.

Graphing the Budget Line

Graphing the budget line involves plotting the combinations of two goods on a coordinate system where one axis represents the quantity of one good and the other axis represents the quantity of the other. The resulting straight line delineates the feasible set of budget allocations and helps visualize the trade-offs between purchasing different items.

Feasible and Infeasible Combinations

Feasible combinations are those that lie on or below the budget line, indicating that the total cost of the items does not exceed the available budget. In contrast, combinations above the budget line are infeasible, as they require spending more than the allocated amount.

Transcript

00:01 Okay, we're given a situation where we want to buy our favorite pet food, but we only have a certain amount of money.

00:11 As a matter of fact, we've got $20 is our entire budget for food.

00:17 And we know that the wet food is $2 a can and the dry food is $4 a bag.

00:29 So we're going to name x, the can, and y, the bag.

00:37 All right? so we're going to turn this into an equation by saying 2x, because each can is $2, we'll have 2x, plus for y, $4 for each y bag is equal to $20, which is our total budget.

00:58 And we want to graph this line.

01:00 The best way to graph a line is to have it in slope intercept form.

01:04 So we're going to solve for y.

01:06 To solve for y, we're going to subtract 2x from both sides of this equation, which will give us 4y is equal to negative 2x plus 20.

01:21 We want to divide everything by 4 as our final set because we want to have y by itself and not have 4y.

01:31 What we end up with as our equation to graph is y is equal to negative one half x plus five.

01:42 Okay, so let's go ahead and form our coordinate plane.

01:57 And we know that five is where we're crossing the y axis.

02:02 That's the y intercept.

02:03 So we'll go up one, two, three, four, five, right? starting from the y intercept, we're going to use our slope...

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