anonymous
  • anonymous
Steve's doctor has advised him to take protein supplements. He bought two brands, Brand A and Brand B. The table gives the amount of calcium, iron, and vitamins (in milligrams per spoonful) in each of the two brands. Brand Calcium Iron Vitamins A 5 4 7 B 4 6 4 Steve needs to take at least 24 milligrams of calcium, 15 milligrams of iron, and 16 milligrams of vitamins. Which ordered pairs of values are solutions for the given system inequalities? Select all the correct answers.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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nincompoop
  • nincompoop
select where?
UsukiDoll
  • UsukiDoll
I think it's misaligned |dw:1436246092831:dw|
anonymous
  • anonymous
yes, it is out of alignment...calcium is 5, iron is 4 and vitamins are 7 for brand A. Brand B has calcium 4, iron is 6 and vitamins are 4. the possible solutions (ordered pairs) are: (1,4) ; (1,5) ; (2,3) ; (3,2) or (4,1)

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ganeshie8
  • ganeshie8
|dw:1436246945999:dw|
ganeshie8
  • ganeshie8
It is given that `Steve needs to take at least 24 milligrams of calcium, 15 milligrams of iron, and 16 milligrams of vitamins` One way to approach this problem is to graph the inequalities corresponding to the 3 inequalities and simply pick the points that belong to common region : \[5A+4B\ge 24\tag{1}\] \[4A+6B\ge 16\tag{2}\] \[7A+4B\ge 15\tag{3}\]
ganeshie8
  • ganeshie8
graphing the inequalities gives us |dw:1436247354463:dw| simply pick the ordered pairs that belong to the common region
ganeshie8
  • ganeshie8
below, the common region is shaded in light blue : |dw:1436247428915:dw| we just need to figure out which ordered pairs fall in this region
ganeshie8
  • ganeshie8
For example, the ordered pair `(1,4)` is not a solution because it doesn't fall in the common region : |dw:1436247749735:dw|
anonymous
  • anonymous
I'm sorry, but I don't see a light blue area on the graph??? If you are looking at the lighter colored purple region, I don't see any of the ordered pairs fitting into this area.
ganeshie8
  • ganeshie8
Thats okay, the actual color is not important at all. Its the common region that you need to figure out from the graphs. Can you plot `(1, 5)` in above graph ?
anonymous
  • anonymous
i think so
ganeshie8
  • ganeshie8
do it
anonymous
  • anonymous
ok, it looks like 1,5 falls w/in the common region of all three lines
ganeshie8
  • ganeshie8
good, so (1,5) is indeed a solution. just so you know, you may click the "pencil" button on top right corner of a drawing to reply.. it actually pastes that drawing in your reply so that you may annotate over it
ganeshie8
  • ganeshie8
|dw:1436248626643:dw|
ganeshie8
  • ganeshie8
How about remaining ordered pairs, do any of them fall in the common region ?
anonymous
  • anonymous
I think 4,1 falls on the line...so would ordered pairs falling on the line be included in the solution set for non-strict inequalities?
ganeshie8
  • ganeshie8
Absolutely! "at least" refers to non-strict inequality, so the boundary points are also part of the solution set.
ganeshie8
  • ganeshie8
|dw:1436249074491:dw|
ganeshie8
  • ganeshie8
|dw:1436249204439:dw|
anonymous
  • anonymous
Thanks for your help! The graph really helped.
ganeshie8
  • ganeshie8
Glad it helped, yw! Btw there is an alternative : You could plugin each of the given ordered pairs into the inequalities and pick the ordered pairs that satisfy all the inequalities. This is more algebra and doesn't give as much insight as the graphs give... But you should also get used to this alternative method as graphing might not be always possible.. good luck!

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