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anonymous

  • one year ago

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.

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  1. nincompoop
    • one year ago
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    select where?

  2. UsukiDoll
    • one year ago
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    I think it's misaligned |dw:1436246092831:dw|

  3. anonymous
    • one year ago
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    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)

  4. ganeshie8
    • one year ago
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    |dw:1436246945999:dw|

  5. ganeshie8
    • one year ago
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    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 : \[5A+4B\ge 24\tag{1}\] \[4A+6B\ge 16\tag{2}\] \[7A+4B\ge 15\tag{3}\]

  6. ganeshie8
    • one year ago
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    graphing the inequalities gives us |dw:1436247354463:dw| simply pick the ordered pairs that belong to the common region

  7. ganeshie8
    • one year ago
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    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

  8. ganeshie8
    • one year ago
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    For example, the ordered pair `(1,4)` is not a solution because it doesn't fall in the common region : |dw:1436247749735:dw|

  9. anonymous
    • one year ago
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    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.

  10. ganeshie8
    • one year ago
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    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 ?

  11. anonymous
    • one year ago
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    i think so

  12. ganeshie8
    • one year ago
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    do it

  13. anonymous
    • one year ago
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    ok, it looks like 1,5 falls w/in the common region of all three lines

  14. ganeshie8
    • one year ago
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    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

  15. ganeshie8
    • one year ago
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    |dw:1436248626643:dw|

  16. ganeshie8
    • one year ago
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    How about remaining ordered pairs, do any of them fall in the common region ?

  17. anonymous
    • one year ago
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    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?

  18. ganeshie8
    • one year ago
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    Absolutely! "at least" refers to non-strict inequality, so the boundary points are also part of the solution set.

  19. ganeshie8
    • one year ago
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    |dw:1436249074491:dw|

  20. ganeshie8
    • one year ago
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    |dw:1436249204439:dw|

  21. anonymous
    • one year ago
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    Thanks for your help! The graph really helped.

  22. ganeshie8
    • one year ago
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    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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