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Systems of Equations & World Problems

  1. Nov 28, 2005 #1
    Question: The weights of two beluga whales and three orca whales totals 36,000 pounds. The weights of one of the belugas and one of the orcas add up to 13,000 pounds. Using this information only, how much do the belugas weigh? How much do the orcas weigh?

    Part 1: Write a system of equations for this problem and solve it by graphing. (You can write 36,000 and 13,000 as 36 and 13 respectively as long as you remember to put the thousand back on in your answer.) You can use the Graphmatica program to create your graphs, or just draw them on paper and fax or mail them to your instructor. Make sure and indicate the intersection on the graph by writing the ordered pair.

    Part 2: Using the same system of equations, solve it by substitution. Be sure to show all work in this process as a final answer is not enough to earn credit. Answer the question in complete sentences.

    Part 3: Solve the same system of equations by the addition method. Again, be sure to show all work and indicate your answers in complete sentences.


    Before reading the questions properly, I had written down something like "2b + 3o = 36,000" and "b + o = 13,000" but "solve it by graphing" (Part 1) threw me off. Would that, what I had down, be right? If so, how do you graph such a thing?
     
  2. jcsd
  3. Nov 29, 2005 #2

    HallsofIvy

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    Since the problem says "You can write 36,000 and 13,000 as 36 and 13 respectively as long as you remember to put the thousand back on in your answer", it might be simpler to write them as b+ 3o= 36 and b+ o= 13 but what you have is fine.

    Do you know that the graphs of equations like these ("linear" equations) are straight lines? Make a "guess" for b and o- they don't have to be values that actually satisfy both equations- b= 0 and o= 0 will work nicely. If you take b= 0 and put it into the equation b+ 3o= 36, you get the equation 3o= 36 so o= 12. Where is the point (0,12) on your graph paper? If you take o= 0 and put it into the equation b+ 3o= 36, you get the equation b= 36. Where is the point (36, 0) on your graph paper? The graph of the equation b+ 3o= 36 is the straight line through those two points.

    Now do the same thing with the other equation: when b= 0, what value of o satifies that equation? Where is that point on your graph paper? When o= 0, what value of b satisfies that equation? Where is that point on your graph paper? Draw the straight line through those points.

    Every point on one line gives b and o values that satisfy one equation. every point on the other line gives b and o values that satisfy the other equation. The point where the two lines intersect lies on both lines and so satisfies both equations.
     
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