Mathematics : asked on valeriegarcia12

01.01.2021

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. which ones are a solution or not to this problem? asap (1, 12) solution or non solution? (2, 10) solution or non solution? (4, 5) solution or non solution? (6, 8.25) solution or non solution? (12, 8) solution or non solution? (18, 6)solution or non solution?

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17.02.2022, solved by verified expert

Nitin Arora

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Mathematics, English, Physics. Research Scholar at Indian Institute of Technology, Roorkee

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Mathematics

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.

Step-by-step answer

P Answered by Master

8 packages

8 jars of sauce

Step-by-step explanation:

As you need just the same amount of pasta and sauce, you only need to create an equation, you can represent the sauce with an x and the pasta with a Y, so your equation would be:

3x + 1y= 36

since X=Y in number your new equation would be:

3x+ 1x=36

4x=36

x= $\frac{36}{9}$

x=9

The other equation would be:

1.5x + 1y= 20

Since x equals y the equation will end up like this:

1.5x+1x=20

2.5x=20

x=8

Since 8 is the number that best suits the needs for the carying capacities, and you´ll end up with 3 extra bucks, but you cant buy the 9 and 9 and then can´t carry them in the backpack.

Mathematics

Step-by-step answer

P Answered by PhD

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

Mathematics

Step-by-step answer

P Answered by Specialist

8 packages

8 jars of sauce

Step-by-step explanation:

As you need just the same amount of pasta and sauce, you only need to create an equation, you can represent the sauce with an x and the pasta with a Y, so your equation would be:

3x + 1y= 36

since X=Y in number your new equation would be:

3x+ 1x=36

4x=36

x= $\frac{36}{9}$

x=9

The other equation would be:

1.5x + 1y= 20

Since x equals y the equation will end up like this:

1.5x+1x=20

2.5x=20

x=8

Since 8 is the number that best suits the needs for the carying capacities, and you´ll end up with 3 extra bucks, but you cant buy the 9 and 9 and then can´t carry them in the backpack.

Mathematics

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 ≥ 0 x + 1.5y ≥ 20 x + 3y ≥ 20 x + 3y ≥ 36 y ≥ 0

Step-by-step answer

P Answered by Master

Your answers would be the first and third choice.

Mathematics

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 ≥ 0 x + 1.5y ≥ 20 x + 3y ≥ 20 x + 3y ≥ 36 y ≥ 0

Step-by-step answer

P Answered by Master

option A: x + 1.5y ≤ 20

option C: x + 3y ≤ 36

option D: x ≥ 0

option H: y ≥ 0

Step-by-step explanation:

It says to assume x = the number of packages of pasta and y = the number of jars of pasta sauce.

Since the number of items can not be a negative number, we have x ≥ 0 and y ≥ 0.

Condition: 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.

If he buys 'x' packs of pasta and 'y' jars of pasta sauce, then:-

Total cost = 1x + 3y ≤ 36 dollars.

and Total weight = 1x + 1.5y ≤ 20 pounds.

Hence, we have four inequalities:-

option A: x + 1.5y ≤ 20

option C: x + 3y ≤ 36

option D: x ≥ 0

option H: y ≥ 0

Mathematics

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)

Step-by-step answer

P Answered by PhD

Given:
limit of $36 and 20 pounds of food in his back pack
pasta : 1 pound package @ $1
pasta sauce: 1.5 pound jar @ $3

x = number of pasta package
y = number of jar of pasta sauce

Constraint on the weight:
x + 1.5y < 20

Constraint on the cost of purchase.
x + 3y < 36

Mathematics

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 ≥ 0 x + 1.5y ≥ 20 x + 3y ≥ 20 x + 3y ≥ 36 y ≥ 0

Step-by-step answer

P Answered by Master

option A: x + 1.5y ≤ 20

option C: x + 3y ≤ 36

option D: x ≥ 0

option H: y ≥ 0

Step-by-step explanation:

It says to assume x = the number of packages of pasta and y = the number of jars of pasta sauce.

Since the number of items can not be a negative number, we have x ≥ 0 and y ≥ 0.

Condition: 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.

If he buys 'x' packs of pasta and 'y' jars of pasta sauce, then:-

Total cost = 1x + 3y ≤ 36 dollars.

and Total weight = 1x + 1.5y ≤ 20 pounds.

Hence, we have four inequalities:-

option A: x + 1.5y ≤ 20

option C: x + 3y ≤ 36

option D: x ≥ 0

option H: y ≥ 0

Mathematics

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) .

Step-by-step answer

P Answered by PhD

Solutions: (2,10), (4,5)

Not solutions: (1,12), (6,10), (12,8), (18,6)

Step-by-step explanation:

Let x be the number of packages of pasta and y be the number of jars of pasta sauce. If pasta costs $1 for a 1-pound package, then x packages of pasta cost $x and weigh x pounds. If pasta sauce costs $3 for a 1.5 pound jar, then y jars cost $3y and weigh 1.5y pounds.

1. Tyler has $36, then

$x+3y\le 36.$

2. Tyler can carry up to 20 pounds of food in his backpack, then

$x+1.5y\le 20.$

You get the following system of inequalities:

$\left\{\begin{array}{l}x+3y\le 36\\ x+1.5y\le 20\end{array}\right.$

Now substitute the coordinates of each point:

(1,12):

$\left\{\begin{array}{l}1+3\cdot 12=37 36\\ 1+1.5\cdot 12=19\le 20\end{array}\right.$

False, because first inequality doesn't hold.

(2,10):

$\left\{\begin{array}{l}2+3\cdot 10=32\le 36\\ 2+1.5\cdot 10=17\le 20\end{array}\right.$

True, both inequalities hold.

(4,5):

$\left\{\begin{array}{l}4+3\cdot 5=19\le 36\\ 4+1.5\cdot 5=11.5\le 20\end{array}\right.$

True, both inequalities hold.

(6,10):

$\left\{\begin{array}{l}6+3\cdot 10=36\le 36\\ 6+1.5\cdot 10=21 20\end{array}\right.$

False, because secondt inequality doesn't hold.

(12,8):

$\left\{\begin{array}{l}12+3\cdot 8=36\le 36\\ 12+1.5\cdot 8=24 20\end{array}\right.$

False, because second inequality doesn't hold.

(18,6):

$\left\{\begin{array}{l}18+3\cdot 6=36\le 36\\ 18+1.5\cdot 6=27 20\end{array}\right.$

False, because second inequality doesn't hold.

Mathematics

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) solution or not a solution (2, 10) solution or not a solution (4, 5) solution or not a solution (6, 10) solution or not a solution (12, 8) solution

Step-by-step answer

P Answered by Master

1,12/ Not a solution

2,10/ solution

4,5/ solution

6,10/ not a solution

12,8/ not a solution

18,6/ not a solution

Step-by-step explanation:

all you have to do is put it into the equation.

for example:

1,12

1x1+12x3= $37

1x1+12x1.5= 19lbs

This is not a solution because he can carry it but doesn't have the money to buy it.

Mathematics

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)

Step-by-step answer

P Answered by PhD

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

Step-by-step 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.