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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. One package of pasta is the right amount to go with one jar of pasta sauce. What is the best numbers of packages of pasta and jars of pasta sauce to buy for the food pantry? How many packages of pasta? How many jars of pasta sauce? Explain your reasoning.

Respuesta :

You start of with $36... & you can only hold 20 lbs...
1+3=4 ($32 left)
1+1.5=2.5 (Can still hold 17.5 lbs.)
1+3=4 ($28 left)
1+1.5=2.5 (Can still hold 15 lbs.)
1+3=4 ($24 left)
1+1.5=2.5 (Can still hold 12.5 lbs.)
1+3=4 ($20 left)
1+1.5=2.5 (Can still hold 10 lbs.)
1+3=4 ($16 left)
1+1.5=2.5 (Can still hold 7.5 lbs.)
1+3=4 ($12 left)
1+1.5=2.5 (Can still hold 5 lbs.)
1+3=4 ($8 left)
1+1.5=2.5 (Can still hold 2.5 lbs.)
1+3=4 ($4 left)
1+1.5=2.5 (You've reached the limit that the back-bag can hold)

So the answer would be 8 packages of pasta & 8 jars of pasta sauce
fichoh

Using the constraint Given to build a model of possible combination of pasta and sauce to purchase, the best estimate of pasta and sauce is 8 respectively.

Given the Parameters and constraints :

  • Maximum amount to spend ≤ $36
  • Maximum capacity ≤20 pounds
  • x = number of pasta packages
  • Cost of x = $1 for 1 pound jar
  • y = number of pasta sauce
  • Cost of y = $3 for 1.5 pound

Since 1 pound of pasta is best to go with 1.5 pounds of sauce

Using trial and error :

5 packages of pasta and 5 jars of sauce

Weight = 5(1) + 5(1.5) = 5 + 7.5 = 12.5 pounds

Cost = 5(1) + 5(3) = 5 + 15 = $20

7 packages of pasta and 7 jars of sauce

Weight = 7(1) + 7(1.5) = 7 + 10.5 = 17.5 pounds

Cost = 7(1) + 7(3) = 7 + 21 = $28

8 packages of pasta and 8 jars of sauce

Weight = 8(1) + 8(1.5) = 5 + 14 = 19 pounds

Cost = 8(1) + 8(3) = 8 + 24 = $32

9 packages of pasta and 9 jars of sauce

Weight = 9(1) + 9(1.5) = 9 + 13.5 = 21.5 pounds (weight exceeded)

Cost = 9(1) + 59(3) = 9 + 27 = 36 pounds

Therefore, we can observe that the best collection of pasta package and sauce to purchase based on the constraint is 8 packages of pasta 8 jars of pasta sauce.

Learn more :https://brainly.com/question/15165519

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