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?

- anonymous

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- 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

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

Thanks much I have a few more would you like more medals?

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## More answers

- anonymous

Don't care about the medals... but will help you... but we will work them together.

- anonymous

i will also help

- 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

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

yea

- anonymous

OK.. what is the other number in the problem that deals with pounds and what do you think the equation is?

- anonymous

240

- anonymous

So what is the equation about pounds.

- anonymous

x+y=240

- anonymous

Good... now we need to deal with the percents.. There are three percents listed. 12%, 6%, and 9%

- anonymous

right

- 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

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

- anonymous

So we have 2 equations ... 2 variables.
x + y = 240
.12x + .06y = .09(240)

- anonymous

x + y = 240
.12x + .06y = 21.60

- 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

ok this is where I dnt understand really I have tried it this way and I dnt get anywhere but the wrong answer.....

- anonymous

x + y = 240
12x + 6y = 2160
OK so far? I will wait for your answer

- anonymous

OOPS same things as multiplying by 100 in the last post

- anonymous

well what happen to 9%?

- 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

right?

- anonymous

What do you mean by right? to what?

- anonymous

I will write what we have right now with every step so it is all together.

- 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

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

ok

- 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

-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

ok gotcha I am trying to follow along sorry

- anonymous

that was easy 120 plus 120 then that would have been more simply

- anonymous

another one ?

- anonymous

Sure

- 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

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

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

ok following

- 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

thanks very much.....rest time

- anonymous

ok

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