Each of the ten volumes of the collected works of Theodore Sturgeon is available in paperback for $\$$15 or in hardcover for $\$$25. Theresa buys a copy of each of the ten volumes for a total of $\$$220. How many hardcover volumes did she buy?
Let me call that number x. Then the number of paperback volumes she bought is 10 - x, since she bought one copy of each volume. The cost of the hardcover volumes is 25x, since each one costs $\$$25. The cost of the paperback volumes is 15(10 - x), since each one costs $\$$15. The total cost of all the volumes is 220, according to the problem. So I have an equation that relates x and the total cost: 25x + 15(10 - x) = 220. I can simplify this equation by distributing the 15 and combining like terms: 25x + 150 - 15x = 220. Then I can subtract 150 from both sides and combine the x terms: 10x = 70. Dividing both sides by 10, I get x = 7. This means that Theresa bought 7 hardcover volumes and 10 - 7 = 3 paperback volumes. 