Question

You have at most $60 to spend on trophies and medals to give as prizes for a contest. A.) Write and graph an inequality that represents the numbers of trophies and medals you can buy. Identify and interpret a solution of the inequality. B.) You want to purchase at least 5 items. Write and graph a system that represents the situation. How many of each item can you buy? Trophies: $10 each. Medals: $6 each.

Answer 1

To represent the number of trophies and medals you can buy, use the inequality 10x + 6y ≤ 60. Graph this inequality and shade the region below the line. For part B, write the system of inequalities x + y ≥ 5 and graph the intersection.

Step-by-step explanation:

To represent the number of trophies and medals you can buy, you should use the inequality: 10x + 6y ≤ 60, where x represents the number of trophies and y represents the number of medals. This inequality represents the total cost of the trophies and medals, which should be less than or equal to $60. To graph this inequality, plot the points on a coordinate plane that satisfy the inequality and shade the region below the line.

To answer part B of the question, if you want to purchase at least 5 items (trophies and/or medals), you can write a system of inequalities: x + y ≥ 5. This ensures that the total number of items is at least 5. To graph this system, plot the points on a coordinate plane that satisfy the inequalities and shade the region that satisfies both inequalities. The intersection of this region will give you the possible number of trophies and medals you can buy.

Answer 2

Cost of a trophy = $10

Cost of a medal = $6

Let the number of trophies that can be bought be t

Let the number of medals that can be bought be m

The maximum amount of money you have to spend = $60

a) The inequality that represents the numbers of trophies and medals that can be bought is:

10t + 6m ≤ 60

The graph of the inequality is plotted below

B) You want to purchase at least 5 items

This means that the total number of trophies and medals bought should be greater than or equal to 5.

The system of inequalities that represents the solution is:

t + m ≥ 5............................(1)

10t + 6m ≤ 60....................(2)

The system of inequalities is graphed below

t + m ≥ 5 is plotted in purple

10t + 6m ≤ 60 is plotted in pink