A couple of years ago during the playoffs, a network sold 30-second ads for $175,000 and 60-second ads for $250,000. If they sold 13 commercial spots and earned $2,650,000, how many of each type of commercial spot did they sell?
you can write this into an equation
# of 30 second ads= x
# of 60 second ads= y
x175,000+y250,000 = 2,650,000
we can turn x+y=13 into x=13-y
and replace x in the second one with such
giving us y250,000 - y175,000 + 2,275,000 = 2,650,000
by subtracting 2,275,000 from both sides and simplifying the left side we are given
y75,000 = 375,000
divide both sides by 75,000
now we plug that into x+y=13
subtract 5 from both sides
which means 8 30 second ads, and 5 60 second ads.