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Claire4christ Group Title

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.

  • 2 years ago
  • 2 years ago

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  1. tcarroll010 Group Title
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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.

    • 2 years ago
  2. Claire4christ Group Title
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    6x12=72

    • 2 years ago
  3. tcarroll010 Group Title
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    Good. Now that you have that number. The initial number that you are starting with is only 15% of that.

    • 2 years ago
  4. Claire4christ Group Title
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    72x0.15

    • 2 years ago
  5. Claire4christ Group Title
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    480

    • 2 years ago
  6. Claire4christ Group Title
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    72/0.15=480

    • 2 years ago
  7. tcarroll010 Group Title
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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.

    • 2 years ago
  8. Claire4christ Group Title
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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.

    • 2 years ago
  9. tcarroll010 Group Title
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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.

    • 2 years ago
  10. Claire4christ Group Title
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    can you help me with this one i dont get it

    • 2 years ago
  11. tcarroll010 Group Title
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    This one is a little harder, but I can definitely help you.

    • 2 years ago
  12. tcarroll010 Group Title
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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.

    • 2 years ago
  13. Claire4christ Group Title
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    ok

    • 2 years ago
  14. Claire4christ Group Title
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    30x0.15=4.5

    • 2 years ago
  15. Claire4christ Group Title
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    i got 3.3 first answer and second one i got 7.2

    • 2 years ago
  16. tcarroll010 Group Title
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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.

    • 2 years ago
  17. Claire4christ Group Title
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    can you put the in one equation little confused

    • 2 years ago
  18. Claire4christ Group Title
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    ok what is next i got this one

    • 2 years ago
  19. Claire4christ Group Title
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    now we have to solve for x right???

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

    • 2 years ago
  21. Claire4christ Group Title
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    i need to know this ______ lbs. of the 15% alloy and ___ lbs. of the 9% alloy.

    • 2 years ago
  22. Claire4christ Group Title
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    there is a third part to this right??? solve for x

    • 2 years ago
  23. Claire4christ Group Title
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    3.3 is the first ansnwer right.

    • 2 years ago
  24. tcarroll010 Group Title
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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?

    • 2 years ago
  25. Claire4christ Group Title
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    y=35

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

    • 2 years ago
  27. Claire4christ Group Title
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    i dont know what you looking for sorry

    • 2 years ago
  28. tcarroll010 Group Title
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    Please read my posts.

    • 2 years ago
  29. Claire4christ Group Title
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    yes i do understand

    • 2 years ago
  30. tcarroll010 Group Title
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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.

    • 2 years ago
  31. Claire4christ Group Title
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    x=21.4

    • 2 years ago
  32. Claire4christ Group Title
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    y=35

    • 2 years ago
  33. Claire4christ Group Title
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    x=3.21 y=3.15

    • 2 years ago
  34. tcarroll010 Group Title
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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.

    • 2 years ago
  35. Claire4christ Group Title
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    will you tell me how you got that

    • 2 years ago
  36. tcarroll010 Group Title
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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.

    • 2 years ago
  37. tcarroll010 Group Title
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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.

    • 2 years ago
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