22. a disc jokey must play 12 commercial spots during 1 hour of a radio show.?

Question

each commercial is either 30 seconds or 60 seconds long. if the total commercial time during 1 hour is 8 minutes, how many 30-second commercials were played that hour? how many 60 second commercials were played?

23. soybean meal is 14% protein;cornmeal is 7% protein. how many pounds of each should be mixed together in order to get 280-lb mixture that is 11% protein?
how many pounds of cornmeal?
how many pounds of soybean?

last question
24. a student makes a $10.25 purchase at a bookstore with a $20 bill. the store has no bills and gives the change in quarters and 50 cent peices, there are 30 coins in all. how many of each kind are there?
quarters?
50 cent peices?

Yves From Canada · Accepted Answer

These 3 problems have the same reasoning. I will do the first one and I will help you to do the others two.

22.
8 minutes is 8*60 = 480 seconds
You have 2 unknown values that we will call :
x = Number of commercials 30 seconds long
y = Number of commercials 60 seconds long
We are searching for "y"

Two unknown values we need two equations.
Let's start with the total number of commercials which is 12 :
x + y = 12
so x = 12 - y

The total time :
30x + 60y = 480
That means number of commercials of 30 second multiplied by 30 seconds PLUS number of commercials of 60 seconds multiplied by 60 second should give you 480 seconds.
In this equation, replace the value of "x" found above :
30x + 60y = 480
30*(12 - y) + 60y = 480
Distribute 30 into the parenthesis :
360 - 30y + 60y = 480
30y = 480 - 360
30 y = 120
y = 120 / 30
y = 4

So you will have 4 commercials of 60 seconds.

PROOF :
To be sure of your answer, always do the proof. To do so, we need the value of "x" :
x = 12 - y
x = 12 - 4
x = 8

30*8 + 60*4 = 480
240 + 240 = 480
480 = 480 :ok


23.
So it is the same. Your unknown values are what you are searching (you can give any letters like "x" and "y" or C and S) :
C = how many pounds of cornmeal
S = how many pounds of soybean

Two unknown values, two equations.
Let's start with the total number of pounds :
C + S = 280
so C = 280 - S

The concentrations :
0.07C + 0.14S = 0.11*280
Replace C with the value found above :
0.07*(280 - S) + 0.14S = 0.11 * 280

Solve this equation and you will find "S". To find "C", just replace the value of "S" in the first equation (C = 280 - S).
At the end, don't forget to do your proves.

Answer is C = 120 and S = 160


24.
First sentence give you the total amount to deal with :
$20 - $10.25 = $9.75

Unknown values :
Q = Quarters
F = Fifty cents pieces

Equation for the total number of coins :
Q + F = 30
Q = 30 - F

Equation of the total value :
0.25Q + 0.50F = 9.75
Replace Q with the value found above :
0.25*(30 - F) + 0.50F = 9.75

Don't forget the decimal points in your calculations.

Answer is Q = 21 and F = 9

22. a disc jokey must play 12 commercial spots during 1 hour of a radio show.?

1 Antwort