SOLUTION: A disc jockey must play 16 commercial spots during 1 hour of a radio show. Each commercial is either 30 seconds or 60 seconds long. If the total commercial time during 1 hour is

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Question 278427: A disc jockey must play 16 commercial spots during 1 hour of a radio show. Each commercial is either 30 seconds or 60 seconds long. If the total commercial time during 1 hour is 13 min, how many 30-second commercials were played that hour? How many 60-second commercials?

Found 2 solutions by richwmiller, Stitch:
Answer by richwmiller(17219) (Show Source):
You can put this solution on YOUR website!
x+y=16
1/2x+y=13
1/2x=3
x=6 30 second spots
y=10 60 second spots
check
6*.5+10=13
6+10=16
ok

Answer by Stitch(470) (Show Source):
You can put this solution on YOUR website!
Let A = 30 sec. Commercial
Let B = 60 Sec. Commercial
*Note I am using Minutes in my equations and not seconds ( 1 min = 60 sec)
Equation 1:
Equation 2: (((0.5A + B = 13}}}
Solution:
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Solve equation 1 for one of the variables. I will solve for B
Equation 1:

Now plug (16 - A) into equation 2 for B
Equation 2: (((0.5A + B = 13}}}
(((0.5A + (16 - A) = 13}}} Simplify
Combine like terms
Subtract 16 from both sides
Divide both sides by -0.5

Now find B by plugging 6 into equation 1 for A
Equation 1:

Check your answer:
-------------------
Plug your values into equation 2 and see if it checks out.
Equation 2: (((0.5A + B = 13}}}
(((0.5*(6) + 10 = 13}}}