A disc Jokey must play 14 commercial spots during 1 hour of a radio show. Each commercial is either 30 or 60 seconds long. If the total commercial time during 1 hour is 11 min, how many 30 second commercials were played during that hour? How many 60 second commercials?
Soybean mean is 16% protein; cornmeal is 8% protein. How many pounds of each should be mixed together in order to get 320-lb mixture that is 12% protein?
A student makes a $8.75 purchase at the bookstore with a $20 bill. The store has no bills and gives the change in quarters and fifty cent pieces. There are 30 coins in all. many quarters are there? How many fifty-cent pieces.
For the first problem
change 11 min to seconds by multiplying by 60. Because there is 60 seconds in one minute.
11 min. * (60 sec./1 min)
= 660 sec.
So for 30 sec. commercial
660/30 = 22 commercial
For 60 sec. commercial
660/60 = 11 commercial
Oops, forgot he wanted to play 14 commercials altogether.
If he did play only 30 sec. commercials he would be over 14.
For both 30 and 60 sec. commercials.
You would have to set up some sort of equation.
let the number of 30 sec commercials be x
then the number of 60 sec commericials is 14-x
11 min = 660 sec
solve : 30x + 60(14-x) = 660
(I get x=6, so 6 short commercials and 8 long ones)
for the second, solve for x
.16x + .08(320-x) = .12(320)
hint: multiply each term by 100 to get rid of decimals
To answer the first question about the number of 30-second and 60-second commercials played during an hour, we can use a system of equations.
Let's assume x represents the number of 30-second commercials and y represents the number of 60-second commercials.
The total number of commercials can be represented by the equation:
x + y = 14
The total commercial time in minutes can be represented by the equation:
0.5x + 1y = 11
We can solve this system of equations to find the values of x and y.
To solve for x, we can multiply both sides of the first equation by 0.5 (to make it consistent with the second equation):
0.5x + 0.5y = 7
Subtracting this equation from the second equation:
(0.5x + 1y) - (0.5x + 0.5y) = 11 - 7
0.5y = 4
Dividing both sides by 0.5:
y = 8
Substituting this value of y back into the first equation:
x + 8 = 14
x = 6
Therefore, there were 6 30-second commercials and 8 60-second commercials played during the hour.
Moving on to the second question about mixing soybean meal and cornmeal to get a 320-lb mixture that is 12% protein.
Let's assume x represents the pounds of soybean meal and y represents the pounds of cornmeal.
The total weight equation:
x + y = 320
The protein percentage equation:
0.16x + 0.08y = 0.12(320)
Simplifying the second equation:
0.16x + 0.08y = 38.4
We can solve this system of equations to find the values of x and y.
Multiplying the first equation by -0.08:
-0.08x - 0.08y = -25.6
Adding this equation to the second equation:
(0.16x - 0.08x) + (0.08y - 0.08y) = 38.4 - 25.6
0.08x = 12.8
Dividing both sides by 0.08:
x = 160
Substituting this value of x back into the first equation:
160 + y = 320
y = 160
Therefore, 160 pounds of soybean meal and 160 pounds of cornmeal should be mixed together to get a 320-lb mixture that is 12% protein.
Moving on to the third question about the number of quarters and fifty-cent pieces given as change.
Let's assume x represents the number of quarters and y represents the number of fifty-cent pieces.
The total value equation:
0.25x + 0.50y = 20 - 8.75
Simplifying the equation:
0.25x + 0.50y = 11.25
We know that there are 30 coins in total, so we have another equation:
x + y = 30
We can solve this system of equations to find the values of x and y.
Multiplying the second equation by -0.25:
-0.25x - 0.25y = -7.5
Adding this equation to the first equation:
(0.25x - 0.25x) + (0.50y - 0.25y) = 11.25 - 7.5
0.25y = 3.75
Dividing both sides by 0.25:
y = 15
Substituting this value of y back into the second equation:
x + 15 = 30
x = 15
Therefore, there are 15 quarters and 15 fifty-cent pieces in the change.