The equation 4x + 5y = 100 models the cost, in dollars, of buying x notebooks at 4 each and y folders at 5 each, for a total of $100. If a…

Substitute $x = 10$ notebooks into $4x + 5y = 100$: $4(10) + 5y = 100$, so $40 + 5y = 100$. Subtract 40: $5y = 60$. Divide by 5: $y = 12$ folders. Check: 10 notebooks cost $40 and 12 folders cost $60, totaling $100. A common wrong answer is 20, which comes from dividing 100 by 5 without accounting for the notebooks. Another is 60, which is the amount of money left for folders but not the number of folders. A third is 15, from subtracting 10 from 25. Divide the leftover money by the price per folder.