a music store is selling compact disks for $11.50 and $7.50. you buy 12 discs and spend a total of $110. how many compact discs that cost $11.50 did you buy?

The first step is to write, $11.50x+$7.50y=$110. Since, y=12-x (Because you bought 12 disks and your subtracting the amount of disks that cost $11.50, you would have to substitute it in) Substitute y in $11.50x+$7.50y=110, so now the problem would be $11.50x+7.50 (12-x) = $110, then use the distributive property so you would get $11.50x+90-7.50x=$110. After that, you would combine the like terms, subtract 7.50x from 11.50x and you get 4x. Now you have 4x+90=$110, so subtract 90 on both sides, and the equation is now 4x=20, so divide both sides by 4, and you get x=5 (number of $11.50 disks.) Now, to find y you can just substitute the x in y=12-x, so it becomes y=12-5 and so y is equal to 7 (amount of $7.50 disks). So, you bought 5 $11.50 compact disks and 7 $7.50 Compact disks.