Question

Tyler went to the supermarket to buy food for a food pantry. He has $36, and can carry up to 20 pounds of food in his backpack.

Pasta costs $1 for a 1-pound package. Pasta sauce costs $3 for a 1.5 pound jar.

Let x = the number of packages of pasta and y = the number of jars of pasta sauce.

Identify each point as either a solution to the system or not a solution to the system of inequalities.

(1, 12)

(2, 10)

(4, 5)

(6, 10)

(12, 8)

(18, 6)

Answer 1

• solutions: (2, 10), (4, 5)
• non-solutions: all other points

Explanation:

It can be useful to graph the inequalities related to Tyler's limits of money and weight.

1x +3y ≤ 36 . . . . . . the limit on the cost of the items Tyler can afford

1x +1.5y ≤ 20 . . . . . the limit on the weight of the items Tyler can carry

Then plotting the given points shows that only (2, 10) and (4, 5) are in the doubly-shaded area that is the solution space. The other points are not a solution.