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A disc jockey must play 14 commercial spots during 1 hour of radio show?

A disc jockey must play 14 commercial spots during 1 hour of radio show. Each commercial is either 30 seconds or 60 seconds long. If the total commercial time during 1 hour is 11 min, how may 30-second commercials were played that hours? How many 60-Second commercials.

Public Comments

  1. 8 (60 sec) 6 (30 sec)
  2. Hi, 8 60-second commercials and 6 30-second commercials take up 11 minutes. <==ANSWER I hope that helps!! :-)
  3. 0.5x + 1y = 11 and x + y = 14 -x -y = -14 ____________ -0.5x = -3 x = 6 y = 8 6 30sec and 8 60 sec commercials
  4. Lets call the 30-second commercials A Lets call the 60-second commercials B The length of a 30-second commercial is .5A minutes (example, one 30-second commercial .5minutes) The length of a 60-second commercial is 1B (example, one 60-second commercial is 1 minute) Now that we have the variables named and the minute-time calculated, we set up a system of equations using A and B: A+B=14 (this equation shows that the number of 30-second commercials added to the number of 60-second commercials is 14) .5A+B=11 (this equation shows that the total airtime of 30-second long and 60-second long commercials is 11 minutes) So, without the descriptions, our system of equations looks like this: A+B=14 .5A+B=11 Now lets multiply the bottom equation by -1. This will leave a +B on the top and a -B on the bottom, so the B's will cancel out, leaving an equation using just A's: A+B=14 -.5A-B= -11 Now lets add the two equations: A+B=14 + -.5A-B= -11 ------------------ .5A=3 A=6 Using A+B=14, we get that 6+B=14, so B=8 There are 6 30-second long commercials and 8 60-second long commercials. CHECK: Lets check that 6 and 8 satisfy our inital equations: 6+8=14 ~~~ CHECK 6*.5+8=11 ~~~ CHECK The equations check out, so there are indeed 6 30-second long commercials and 8 60-second long commercials. ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ If you need further explanation or any other help, feel free to ask.
  5. x+y=14 .5x+y=11 (.5 for the 30 second ones, the 60 second ones are "1y" rewrite the first equation as y=14-x and substitute into the second equ. .5x+(14-x)=11 .5x+14-x=11 -.5x= -3 x=6, so there are 6 thirty second ads and 14-6=8 one minute ads checks6*.5 minute + 8*1 minute=3+8=11. so it works
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