Question

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?

Answer 1

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

Answer 2

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

Answer 3

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

Answer 4

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

Answer 5

i will also help

Answer 6

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?

Answer 7

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?

Answer 8

yea

Answer 9

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

Answer 10

240

Answer 11

So what is the equation about pounds.

Answer 12

x+y=240

Answer 13

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

Answer 14

right

Answer 15

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.

Answer 16

so

.12x + .06y = .09(240)

12% of the soybean + 6% of the cornmeal will give you 240 pounds of 9% protein.

OK

Answer 17

So we have 2 equations ... 2 variables.

x + y = 240
.12x + .06y = .09(240)

Answer 18

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

Answer 19

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

Answer 20

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

Answer 21

x + y = 240
12x + 6y = 2160

OK so far? I will wait for your answer

Answer 22

OOPS same things as multiplying by 100 in the last post

Answer 23

well what happen to 9%?

Answer 24

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

Answer 25

right?

Answer 26

What do you mean by right? to what?

Answer 27

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

Answer 28

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.

Answer 29

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???

Answer 30

ok

Answer 31

Sorry I am not feeling good and I am trying to get these last few done so that I can go get some rest....

Answer 32

-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

Answer 33

ok gotcha I am trying to follow along sorry

Answer 34

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

Answer 35

another one ?

Answer 36

Sure

Answer 37

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?

Answer 38

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

Answer 39

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)

Answer 40

ok following

Answer 41

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.

Answer 42

thanks very much.....rest time

Answer 43

ok