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.
Select all that apply.

Choose the inequalities needed to describe the amount of pasta and pasta sauce that Tyler can buy.
(x + 1.5y ≤ 20) (x + 1.5y ≤ 36) (x + 3y ≤ 36) (x ≥ 0x + 1.5y ≥ 20) (x + 3y ≥ 20) x + 3y ≥ 36 ) (y ≥ 0)

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.
Select all that apply.

Choose the inequalities needed to describe the amount of pasta and pasta sauce that Tyler can buy.
(x + 1.5y ≤ 20)    (x + 1.5y ≤ 36) (x + 3y ≤ 36)     (x ≥ 0x + 1.5y ≥ 20) (x + 3y ≥ 20) x + 3y ≥ 36 )    (y ≥ 0)

ddcamp · Answer

There are two parameters:
The weight can't exceed 20 pounds.
The cost can't exceed $36.

What would the equation for the total cost spent be (if x=packages of pasta and y=jars of sauce)?

anonymous · Answer

The 1st and 3rd choice?

ddcamp · Answer

Yup!

anonymous · Answer

thats all?

ddcamp · Answer

Though you may also need y≥0 and x≥0 (because you can't buy negative jars of sauce of packages of pasta.)

anonymous · Answer

can you help me with one more?

ddcamp · Answer

Sure

anonymous · Answer

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.

ddcamp · Answer

Find the greatest number where you have equal amounts of both pasta and sauce. This will be a good point because the food pantry will get the most food without having too little pasta or sauce.

anonymous · Answer

Eight is the best numbers of packages of pasta and jars of pasta sauce to buy for the food pantry.  

 Eight packages of pasta.   Eight jars of pasta sauce. 
 
Eight is the best numbers of packages of pasta and jars of pasta sauce to buy for the food pantry because 8 dollars of pasta package equals exactly 8 pounds.  

Pasta sauce costs $3 for a 1.5 pound jar which means I have to multiply $3 x the number 8 which equals $24.

 Now I have to multiply 1.5 x 8 which equals 12 pounds.

 (The weight can't exceed 20 pounds.) (The cost can't exceed $36.) 8 pounds of pasta + 12 pounds of pasta sauce (20 pounds). $8 of pasta + $24 of pasta sauce = ($32.)  correct?