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Claire4christ

somebody please help me with this question. Mr. Thompson has been asked to add storage space to a garage. He estimates 6 square feet per individual will be required to meet the needs of 12 people. If the storage space is 15% of the total amount of space required, how much total space does Mr. Thompson have? Mr. Thompson had______ square feet.

  • one year ago
  • one year ago

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  1. tcarroll010
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    A good start is to see how much total storage space is required. So, that part is given by 6 square feet for each person and there are 12 people.

    • one year ago
  2. Claire4christ
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    6x12=72

    • one year ago
  3. tcarroll010
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    Good. Now that you have that number. The initial number that you are starting with is only 15% of that.

    • one year ago
  4. Claire4christ
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    72x0.15

    • one year ago
  5. Claire4christ
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    480

    • one year ago
  6. Claire4christ
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    72/0.15=480

    • one year ago
  7. tcarroll010
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    Yes, and you are answering your own questions beautifully, which is the goal. Except that you have to multiply out 72 by 0.15 to get 10.8. So, yes to your first of the 3 answers above.

    • one year ago
  8. Claire4christ
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    An alloy weighing 30 lbs. is 11% tin. The alloy was made by mixing a 15% tin alloy and a 9% tin alloy. How many pounds of each alloy were used to make the 11% alloy? ___ lbs. of the 15% alloy and ___ lbs. of the 9% alloy.

    • one year ago
  9. tcarroll010
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    The 15% is basically saying that he needs 72, but he only has 15% of that to start with, so by eyeballing the 72 x 0.15, we know that it will be a fairly small number. For checking.

    • one year ago
  10. Claire4christ
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    can you help me with this one i dont get it

    • one year ago
  11. tcarroll010
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    This one is a little harder, but I can definitely help you.

    • one year ago
  12. tcarroll010
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    A lot of problems like this are made easier by first correctly conceptualizing the problem, and then the math is actually the easier part. We start by asking how much tin is actually in the 30 lbs. In 30 lbs., we have 0.11 of it as tin, so we have 30 x 0.11 lbs. or 3.3 lbs. Believe it or not, that's half the problem done.

    • one year ago
  13. Claire4christ
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    ok

    • one year ago
  14. Claire4christ
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    30x0.15=4.5

    • one year ago
  15. Claire4christ
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    i got 3.3 first answer and second one i got 7.2

    • one year ago
  16. tcarroll010
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    Now, let's call the 15% alloy as x lbs. and the 9% alloy as y lbs. The total weight we know from the problem is 30 lbs. So, we know that x + y = 30 because that is the total weight. We also know that (x)(0.15) + (y)(0.09) = 3.3 because we know we have 3.3 lbs. of tin total. So, we have 2 equations in 2 unknowns.

    • one year ago
  17. Claire4christ
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    can you put the in one equation little confused

    • one year ago
  18. Claire4christ
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    ok what is next i got this one

    • one year ago
  19. Claire4christ
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    now we have to solve for x right???

    • one year ago
  20. tcarroll010
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    So, are you ok with the 2 equations in the 2 unknowns, or are you stuck at this point?

    • one year ago
  21. Claire4christ
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    i need to know this ______ lbs. of the 15% alloy and ___ lbs. of the 9% alloy.

    • one year ago
  22. Claire4christ
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    there is a third part to this right??? solve for x

    • one year ago
  23. Claire4christ
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    3.3 is the first ansnwer right.

    • one year ago
  24. tcarroll010
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    Yes, that's from the problem statement. You have x + y = 30 and you have (0.15)x + (0.09)y = 3.3 These are your 2 equations for going forward with the problem. What I am asking is if you understand the derivation of the equations and the steps up to this point. Plus, a second question is are you able to solve simultaneous equations. I asked 2 questions. What are your 2 answers?

    • one year ago
  25. Claire4christ
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    y=35

    • one year ago
  26. tcarroll010
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    I'm looking for 2 yes/no answers at this point. Then we can proceed.

    • one year ago
  27. Claire4christ
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    i dont know what you looking for sorry

    • one year ago
  28. tcarroll010
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    Please read my posts.

    • one year ago
  29. Claire4christ
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    yes i do understand

    • one year ago
  30. tcarroll010
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    So, then all that is left is to solve the simultaneous equations for x and y, and from your last answer, you indicate that you are able to do that.

    • one year ago
  31. Claire4christ
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    x=21.4

    • one year ago
  32. Claire4christ
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    y=35

    • one year ago
  33. Claire4christ
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    x=3.21 y=3.15

    • one year ago
  34. tcarroll010
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    Your 2 simultaneous equations are x + y = 30 and (0.15)x + (0.09)y = 3.3. Solving the first equation for x, we have x = 30 - y. We substitute that into the second equation and solve for y. Y=20. We go back to the first equation with that y and find that x=10. So, 10 lbs. of the 15% alloy and 20 lbs. of the 9% alloy. And that's your answer.

    • one year ago
  35. Claire4christ
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    will you tell me how you got that

    • one year ago
  36. tcarroll010
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    (0.15)x + (0.09)y = 3.3 -> (0.15)(30-y) + (0.09)y = 3.3. And solve for y. This is a little bit more detail flowing from my previous post.

    • one year ago
  37. tcarroll010
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    (0.15)(30-y) + (0.09)y = 3.3 -> 4.5 - (0.15)y + (0.09)y = 3.3. Combine y's.

    • one year ago
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