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feedmemikey

  • 2 years ago

A sporting goods store has added a section with trail foods and snacks. Raisins cost $5.00 per pound and peanuts cost $3.80 per pound. Raisins and peanuts are going to be sold in a mixture of 30 pounds which will cost $4.05 per pound? How many pounds of raisins will be in the mix?

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  1. feedmemikey
    • 2 years ago
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    My education in math basically stopped at 6th grade. Could someone help me, please? I feel exremely stupid for not understanding what I am to do about this problem.

  2. gandalfwiz
    • 2 years ago
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    Dang, mixture problems. I'm in an 11th grade math course, we did this at the begginning of the year, and I've completely forgotten. I'm sure you're not the only one :) Let me pull out my old books...

  3. satellite73
    • 2 years ago
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    \[5x+3.80(30-x)=30\times 4.05\] solve for x

  4. feedmemikey
    • 2 years ago
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    That is just numbers to me. Please take it step by step.

  5. satellite73
    • 2 years ago
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    reason as follows put x as the pounds of raisins then since the total is 30 pounds, the number of pounds of peanuts must be 30- x

  6. feedmemikey
    • 2 years ago
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    I multiply 30 by x? What is x?

  7. satellite73
    • 2 years ago
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    you want 30 pounds of mixute that cost 4.05 per pound, so the total cost should be \[4.05\times 30 = 112.50\]

  8. satellite73
    • 2 years ago
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    hold on lets start again slowly

  9. feedmemikey
    • 2 years ago
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    Okay.

  10. satellite73
    • 2 years ago
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    you are looking for what? two numbers. one is the number of pounds of raisins the other is the number of pounds of peanuts

  11. satellite73
    • 2 years ago
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    you don't know either of these two numbers, so you first need to name a variable, and the variable should be one of the two numbers. i used x, you can use whatever you like you should write down what your variable represents i write "let x be the number of pounds of raisins"

  12. satellite73
    • 2 years ago
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    now i know that if we have "x" pounds of raisins we must have \[30-x\] pounds of peanuts. why? because the total is 30 so for example if you have 5 pounds of raisins you would have 25 pounds of peanuts, and if you had 10 pounds of raising you would need 20 pounds of peanuts, and more generally if you have "x" pounds of raisins you must have \[30-x\] pounds of peanuts

  13. satellite73
    • 2 years ago
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    how are we doing so far?

  14. satellite73
    • 2 years ago
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    ?

  15. feedmemikey
    • 2 years ago
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    So, I am to find what x is? So x is less than 30?

  16. satellite73
    • 2 years ago
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    you wrote "Raisins and peanuts are going to be sold in a mixture of 30 pounds..."

  17. satellite73
    • 2 years ago
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    that means that the total is 30

  18. feedmemikey
    • 2 years ago
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    Yes, but you wanted me to take x away from 30, so x is less than 30, no?

  19. satellite73
    • 2 years ago
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    when i wrote \[30-x\] is the number of pounds of peanuts, that is because the pounds of peanuts and the pounds of raisins have to add to 30

  20. satellite73
    • 2 years ago
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    yes both numbers must be less than 30 because you will have 30 pounds total

  21. feedmemikey
    • 2 years ago
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    Alright.

  22. satellite73
    • 2 years ago
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    now rasins cost $5 a pound if you have 2 pounds of raisins it will cost $10 if you have 4 pounds of raisins it will cost $20 if you have 7 pounds of raisins it will cost $35 more generally if you have x pounds of raisins it will cost 5x dollars

  23. feedmemikey
    • 2 years ago
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    Okay. I understand what you wrote.

  24. satellite73
    • 2 years ago
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    likewise if you have \[30-x\] pounds of peanuts, because they cost $3.80 a pound the total cost will be \[3.80\times (30-x)\] for the peanuts

  25. feedmemikey
    • 2 years ago
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    Right.

  26. satellite73
    • 2 years ago
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    now we write down what the total cost will be two different ways. one was is easy we have 30 pounds and the cost per pound is $4.05 (because you are told) "30 pounds which will cost $4.05 per pound"

  27. feedmemikey
    • 2 years ago
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    So I multiply $4.05 until I get $30?

  28. satellite73
    • 2 years ago
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    so we multiply to get the total cost. it must be \[4.05]\times 30 =\$121.50\]

  29. satellite73
    • 2 years ago
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    no you multiply the cost per pound times the number of pounds

  30. satellite73
    • 2 years ago
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    you know you have 30 pounds you know it cost $4.05 per pound so you know the total cost will be $121.50 by multiplication

  31. satellite73
    • 2 years ago
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    so we actually know what the total cost is, it is number we can compute

  32. feedmemikey
    • 2 years ago
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    What do they want me to find? The amount (money-wise) it takes for raisins to get to 30 lbs.?

  33. satellite73
    • 2 years ago
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    on the other hand, we have an expression for the cost of the raisins. that expression is \[5x\] and we also have an expression for the total cost of the peanuts, that expression is \[3.80(30-x)\] so another expression for the total of both is what you get when you add them up namely \[5x+3.80(30-x)\]

  34. satellite73
    • 2 years ago
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    no go back and make sure you remember what the problem is asking for "how many pounds..."

  35. feedmemikey
    • 2 years ago
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    This is much too complicated for me, I'm sorry.

  36. satellite73
    • 2 years ago
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    so we have two expressions for the total cost, one is \[5x+3.80(30-x)\] the other is 121.50 so write \[5x+3.08(30-x)=121.50\] and solve for x

  37. feedmemikey
    • 2 years ago
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    Like I said, I stopped progressing in math at 6th grade. I'm technically in 11th grade now.

  38. satellite73
    • 2 years ago
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    ok well all the steps are there, that is i wrote them all down. if you have time see if you can understand what the steps entail and why they work the way they do on the other hand if you cannot solve the above equation we are truly stuck. good luck

  39. feedmemikey
    • 2 years ago
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    I'm sorry for wasting your time. I'm a dead end when it comes to math :(

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