Question

Julian and his children went into a restaurant where they sell hotdogs for $4.50 each and

drinks for $1.75 each. Julian has $35 to spend and must buy no less than 12 hotdogs and
drinks altogether. Also, he must buy at least 2 hotdogs. If a represents the number of hotdogs
purchased and y represents the number of drinks purchased, write and solve a system of
inequalities graphically and determine one possible solution.
Number of Inequalities: 3

Answer 1

Step-by-step explanation:

The system of inequalities can be written as:

a ≥ 2 (buy at least 2 hotdogs)

a + y ≥ 12 (buy no less than 12 hotdogs and drinks altogether)

4.5a + 1.75y ≤ 35 (stay within the budget of $35)

To solve this graphically, we can plot the boundary lines for each inequality and shade the feasible region where all three conditions are satisfied.

First, plot the boundary line for a = 2. This is a vertical line passing through a = 2 on the x-axis.

Next, plot the boundary line for a + y = 12. This is a diagonal line passing through (0,12) and (12,0) on the coordinate plane.

Finally, plot the boundary line for 4.5a + 1.75y = 35. This is a diagonal line passing through (7.78, 0) and (0, 20) on the coordinate plane. (To find these points, solve for a or y in terms of the other variable and substitute values to get two points.)

The feasible region is the shaded area where all three boundary lines intersect. One possible solution within this region is (a=6, y=6). Julian could buy 6 hotdogs and 6 drinks for a total cost of $33, which is within his budget of $35.

Answer 2

To solve this problem, we can set up a system of inequalities and graphically find the feasible region to determine one possible solution.

Step-by-step explanation:

To solve this problem, we can set up a system of inequalities based on the given conditions. Let's define 'a' as the number of hotdogs purchased and 'y' as the number of drinks purchased. The inequalities are as follows:

1. a + y >= 12 (At least 12 hotdogs and drinks altogether)
2. a >= 2 (At least 2 hotdogs)
3. 4.50a + 1.75y <= 35 (Julian has $35 to spend)

We can graph these inequalities on a coordinate plane to find the feasible region where the solutions lie. The shaded area that satisfies all three inequalities is the feasible region. From the graph, we can read off one possible solution or coordinate point that satisfies all three inequalities.