Helppppppppppppppppppp

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.

sattari [20]

Answer:

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.

7 0

2 years ago

3) Tara sold candles to raise money for new playground equipment at her school.

Ronch [10]

Answer:

Tara's current expression finds how much the school will be keeping. 50 x 2/5 (also written as 50 x 0.4) totals out as 20. $20 is 2/5 of $50. The expression that Tara SHOULD have written to find how much goes to the candle company would be 50 x 3/5 (also written as 50 x 0.6), as this adds up to 30. $30 is 3/5 of $50.

Step-by-step explanation:

50/5 = 10 which means that 1/5 of 50 = 10.

2/5 of 50 ($20) is kept by the school. This is what Tara's expression finds. This means that $30 is sent to the candle company, and can be found with the expression 50 x 3/5.

The decimals are created by dividing the numerator of the fraction by the denominator (I find it easier to do math with decimals).

3 0

2 years ago

Ilsym!!!!! help thanks so much

kolezko [41]

Answer:

A w is less than 7

A x is greater then or equal to -1

Step-by-step explanation:

7 0

2 years ago

Read 2 more answers

To which subset of real numbers does the number 1/5 belong

Travka [436]

1/5 is an expression that represents 1÷5= .2
Since the return decimal equivalent doesn't go on forever and has a finite end, this is a member of the rational number set.

4 0

2 years ago

Which two ratios represent quantities that are proportional?

vesna_86 [32]

Answer:

B

Step-by-step explanation:

4 0

2 years ago