anonymous
  • anonymous
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?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
anonymous
  • anonymous
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
anonymous
  • anonymous
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
anonymous
  • anonymous
Thanks much I have a few more would you like more medals?

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anonymous
  • anonymous
Don't care about the medals... but will help you... but we will work them together.
anonymous
  • anonymous
i will also help
anonymous
  • anonymous
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?
anonymous
  • anonymous
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?
anonymous
  • anonymous
yea
anonymous
  • anonymous
OK.. what is the other number in the problem that deals with pounds and what do you think the equation is?
anonymous
  • anonymous
240
anonymous
  • anonymous
So what is the equation about pounds.
anonymous
  • anonymous
x+y=240
anonymous
  • anonymous
Good... now we need to deal with the percents.. There are three percents listed. 12%, 6%, and 9%
anonymous
  • anonymous
right
anonymous
  • anonymous
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.
anonymous
  • anonymous
so .12x + .06y = .09(240) 12% of the soybean + 6% of the cornmeal will give you 240 pounds of 9% protein. OK
anonymous
  • anonymous
So we have 2 equations ... 2 variables. x + y = 240 .12x + .06y = .09(240)
anonymous
  • anonymous
x + y = 240 .12x + .06y = 21.60
anonymous
  • anonymous
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
anonymous
  • anonymous
ok this is where I dnt understand really I have tried it this way and I dnt get anywhere but the wrong answer.....
anonymous
  • anonymous
x + y = 240 12x + 6y = 2160 OK so far? I will wait for your answer
anonymous
  • anonymous
OOPS same things as multiplying by 100 in the last post
anonymous
  • anonymous
well what happen to 9%?
anonymous
  • anonymous
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
anonymous
  • anonymous
right?
anonymous
  • anonymous
What do you mean by right? to what?
anonymous
  • anonymous
I will write what we have right now with every step so it is all together.
anonymous
  • anonymous
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.
anonymous
  • anonymous
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???
anonymous
  • anonymous
ok
anonymous
  • anonymous
Sorry I am not feeling good and I am trying to get these last few done so that I can go get some rest....
anonymous
  • anonymous
-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
anonymous
  • anonymous
ok gotcha I am trying to follow along sorry
anonymous
  • anonymous
that was easy 120 plus 120 then that would have been more simply
anonymous
  • anonymous
another one ?
anonymous
  • anonymous
Sure
anonymous
  • anonymous
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?
anonymous
  • anonymous
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
anonymous
  • anonymous
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)
anonymous
  • anonymous
ok following
anonymous
  • anonymous
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.
anonymous
  • anonymous
thanks very much.....rest time
anonymous
  • anonymous
ok

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