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anonymous

  • 5 years ago

A disc must play 14 commerical spots during 1 hour of a radio show. Each commerical is either 30 seconds or 60 seconds long. If the total commercial time during 1 hour is 11min, how many 30 second commercials were played that hour? How many 60 second commercials?

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  1. anonymous
    • 5 years ago
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    let x be no. of commer. of 30 sec and y be of 60 so x*30+y*60=11*60 and x+y=14 solve 2 equations

  2. anonymous
    • 5 years ago
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    x = number of 30 second spots y = number of 60 second spots x + y = 14 30x + 60y = 660 11(60) = 660 seconds -30x - 30y = -420 30x + 60y = 660 30y = 240 y = 8 x + 8 = 14 x = 6 6 30 second spots 8 60 second spots

  3. anonymous
    • 5 years ago
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    Thanks much I have a few more would you like more medals?

  4. anonymous
    • 5 years ago
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    Don't care about the medals... but will help you... but we will work them together.

  5. anonymous
    • 5 years ago
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    i will also help

  6. anonymous
    • 5 years ago
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    Soybean meal is 12% protein; cornmeal is 6% protein. How many pounds of each should be mixed together in order to get 240 pounds mixture that is 9% protein?

  7. anonymous
    • 5 years ago
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    First of all you should see we are talking about two different concepts (pounds and percents) we will start with pounds. x = pounds of soybean meal y = pounds of cornmeal OK so far?

  8. anonymous
    • 5 years ago
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    yea

  9. anonymous
    • 5 years ago
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    OK.. what is the other number in the problem that deals with pounds and what do you think the equation is?

  10. anonymous
    • 5 years ago
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    240

  11. anonymous
    • 5 years ago
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    So what is the equation about pounds.

  12. anonymous
    • 5 years ago
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    x+y=240

  13. anonymous
    • 5 years ago
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    Good... now we need to deal with the percents.. There are three percents listed. 12%, 6%, and 9%

  14. anonymous
    • 5 years ago
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    right

  15. anonymous
    • 5 years ago
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    of the mixture 12% of it is soybean protein of the mixture 6% of it is cornmeal protein and we want to mix it to be 9% protein.

  16. anonymous
    • 5 years ago
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    so .12x + .06y = .09(240) 12% of the soybean + 6% of the cornmeal will give you 240 pounds of 9% protein. OK

  17. anonymous
    • 5 years ago
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    So we have 2 equations ... 2 variables. x + y = 240 .12x + .06y = .09(240)

  18. anonymous
    • 5 years ago
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    x + y = 240 .12x + .06y = 21.60

  19. anonymous
    • 5 years ago
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    I like to multiply every term by something to get rid of decimals... or multiplying means the same thing as moving the decimal. so I am going to move the decimal two to the right on every term... same thing as multiplying by 10

  20. anonymous
    • 5 years ago
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    ok this is where I dnt understand really I have tried it this way and I dnt get anywhere but the wrong answer.....

  21. anonymous
    • 5 years ago
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    x + y = 240 12x + 6y = 2160 OK so far? I will wait for your answer

  22. anonymous
    • 5 years ago
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    OOPS same things as multiplying by 100 in the last post

  23. anonymous
    • 5 years ago
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    well what happen to 9%?

  24. anonymous
    • 5 years ago
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    I took the 9% times the 240 because at the end you want 240 pounds that is 9% protein. If you look above I had .09(240) which is 21.6

  25. anonymous
    • 5 years ago
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    right?

  26. anonymous
    • 5 years ago
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    What do you mean by right? to what?

  27. anonymous
    • 5 years ago
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    I will write what we have right now with every step so it is all together.

  28. anonymous
    • 5 years ago
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    x + y = 240 .12x + .06y = .09(240) I am going to multiply .09 * 240 x + y = 240 .12x + .06y = 21.6 I am going to multiply each term by 100 x + y = 240 12x + 6y = 2160 Now is when we have to get rid of one of the letters. We can get rid of the x's or the y's. I am going to pick the y's because the 6 with the y is smaller than the 12 with the x.

  29. anonymous
    • 5 years ago
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    The way we do that is to multiply one equation by some number that will get a variable that will cancel out so that we are only left with one variable. for example 6y - 6y = 0 another example -6y + 6y = 0 SO -6(x + y = 240) which when we distribute is -6x - 6y = -1440 OK???

  30. anonymous
    • 5 years ago
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    ok

  31. anonymous
    • 5 years ago
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    Sorry I am not feeling good and I am trying to get these last few done so that I can go get some rest....

  32. anonymous
    • 5 years ago
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    -6x - 6y = -1440 12x + 6y = 2160 Notice the y's are going to cancel out when we add 6x = 720 (I added the two equations together) x = 120 (I divided by 6) So if x = 120 and our first equation said x + y = 240 then 120 + y = 240 y = 120 so x = 120 and y = 120 120 pounds of soybeans and 120 pounds of cornmeal

  33. anonymous
    • 5 years ago
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    ok gotcha I am trying to follow along sorry

  34. anonymous
    • 5 years ago
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    that was easy 120 plus 120 then that would have been more simply

  35. anonymous
    • 5 years ago
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    another one ?

  36. anonymous
    • 5 years ago
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    Sure

  37. anonymous
    • 5 years ago
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    A student makes a $9.75 purchase at the bookstore with a $20 bill. The store has no bills and give change in quarter and fifty cents pieces. There are 30 coins in all. How many of each kind are there?

  38. anonymous
    • 5 years ago
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    Two concepts number of coins and money. x = number of quarters y = number of 50 cent pieces. So since we have 30 coins we have x + y = 30

  39. anonymous
    • 5 years ago
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    Money wise we know that each quarter has a value of .25 so if you had 5 of them it would be worth .25 * 5 but in this problem we have x of them so the value is .25x same with the 50 cent pieces.. so .25x + .50y = 10.25 (we need the amount of change 20 - 9.75)

  40. anonymous
    • 5 years ago
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    ok following

  41. anonymous
    • 5 years ago
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    x + y = 30 .25x + .50y = 10.25 (multiply second equation by 100 to get rid of decimals) x + y = 30 25x + 50y = 1025 I am going to get rid of the x's by multiplying by -25 -25(x + y = 30) 25x + 50y = 1025 -25x - 25y = -750 25x + 50y = 1025 add the two equations. 25y = 275 (the x's canceled out) y = 11 so we had 11 50 cent pieces. Our first equation said x + y = 30 so x + 11 = 30 x = 19 so we had 19 quarters.

  42. anonymous
    • 5 years ago
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    thanks very much.....rest time

  43. anonymous
    • 5 years ago
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    ok

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