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.
Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga.
Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus.
Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
I think it's misaligned
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)
Not the answer you are looking for? Search for more explanations.
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 :
graphing the inequalities gives us
simply pick the ordered pairs that belong to the common region
below, the common region is shaded in light blue :
we just need to figure out which ordered pairs fall in this region
For example, the ordered pair `(1,4)` is not a solution because it doesn't fall in the common region :
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.
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 ?
i think so
ok, it looks like 1,5 falls w/in the common region of all three lines
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
How about remaining ordered pairs, do any of them fall in the common region ?
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?
Absolutely! "at least" refers to non-strict inequality, so the boundary points are also part of the solution set.
Thanks for your help! The graph really helped.
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!