Question 148366
a disc jockey must play 14 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 11 minutes how many 30 second commercials were played that hour?  How many 60 second commercials?


the total commercial time during 1 hour is 11 minutes
Convert 11 minutes to seconds
660 seconds


x=amount of 30 second commercials
y=amount of 60 second commercials


30x+60y=660


a disc jockey must play 14 commercials


x+y=14


So you have 

{{{30x+60y=660}}}
{{{x+y=14}}}


Use the second equation and solve for x.

{{{x+y=14}}} becomes {{{x=14-y}}}


Plug that in for x in the first equation.
{{{30(14-y)+60y=660}}}


Distribute
{{{420-30y+60y=660}}}


Combine like terms
{{{420+30y=660}}}


Subtract 420 from both sides
{{{30y=240}}}


Divide by 30
{{{y=8}}}


plug that in for y in the second original equation
{{{x+8=14}}}
{{{x=6}}}


Check: {{{30x+60y=660}}}
{{{30(6)+60(8)=660}}}
{{{180+480=660}}}
It's true!


So the dj played 6 thirty-second commercials and 8 sixty-second commercials