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

let's review what we know so far:
1. he has 36 dollars
2. he can only carry up to 20 lbs of food
3. pasta costs 1 dollar per package, and weighs 1 lb per package
4. pasta sauce costs 3 dollars per jar, and weighs 1.5 lb per package
5. we are supposed to use x to represent the number of pasta packs and y to represent the jars of sauce

using the weight information:
the total weight from x packages of pasta sauce is simply 1*x, or just x
the total weight from y packages of sauce is 1.5*y

he can only carry 20 lbs, so

x + 1.5y ≤ 20

using the cost information:
the cost of x packages of pasta is 1*x, or just x
the cost of y packages of sauce is 3*y

he can only spend 36 dollars, so

x + 3y ≤ 36

Answer 2

your system is:

x + 1.5y ≤ 20
x + 3y ≤ 36

and you are given a series of x and y coordinates to test. you should plug each coordinate into both inequalities. if both inequalities are satisfied (are true) then the point is a solution to the system, and should be included as part of your solution. otherwise, leave that point out of your solution.