A music dealer ran a sale of records and tapes. Records were reduced to $7 each and tapes to $7.50 each. The dealer sold 60 more records than tapes for a total sale of $2160. How many records did the dealer sell?

First, let's call the number of records sold: #r#

And, let's call the number of tapes sold: #t#

From the information in the problem we can write two equations:

Equation 1: We know 60 more records we sold than tapes so we can write:

#r = t + 60#

Equation 2: We know the cost of records and tapes and we know how much total money was collected from the sales of both so we can write:

#$7.00r + $7.50t = $2160#

Step 1) Solve the first equation for #t#:

#r = t + 60#

#r - color(red)(60) = t + 60 - color(red)(60)#

#r - 60 = t + 0#

#r - 60 = t#

#t = r - 60#

Step 2) We can now substitute #(r - 60)# for #t# in the second equation and solve for #r#:

#$7.00r + $7.50t = $2160# becomes:

#$7.00r + $7.50(r - 60) = $2160#

#$7.00r + $7.50r - $450.00 = $2160#

#($7.00 + $7.50)r - $450.00 = $2160#

#$14.50r - $450.00 = $2160#

#$14.50r - $450.00 + color(red)($450.00) = $2160 + color(red)($450.00)#

#$14.50r - 0 = $2610.00#

#$14.50r = $2610.00#

#($14.50r)/color(red)($14.50) = ($2610.00)/color(red)($14.50)#

#(color(red)(cancel(color(black)($14.50)))r)/cancel(color(red)($14.50)) = (color(red)(cancel(color(black)($)))2610.00)/color(red)(color(black)(cancel(color(red)($)))14.50)#

#r = 2610.00/14.50#

#r = 180#

The Answer Is: 180 records we sold