Hillary has eleven coins, all dimes and nickels. In total, the coins are worth 75 cents. How many nickels does she have?
I need to find the number of nickels, which I'll call n. Then the number of dimes must be 11 - n, since she has eleven coins in total. Each nickel is worth 5 cents, and each dime is worth 10 cents. So the total value of the coins is 5n + 10(11 - n). This value has to equal 75 cents, so I can set up an equation: 5n + 10(11 - n) = 75. I can start by expanding the parentheses: 5n + 110 - 10n = 75. Then I can combine like terms: -5n + 110 = 75. Next, I can subtract 110 from both sides: -5n = -35. Finally, I can divide both sides by -5: n = 7. 