
Example: Jill has 26 coins in her purse. They are all dollar and quarter coins. If they add up to $18.50. How many of each coin does she have. Solution: Let 'd' stand for the number of dollar coins and 'q' stand for the number of quarters. The rest of the coins are quarters. Jill has 26 coins in her purse. They are all dollar and quarter coins. Then d + q = 26 1 dollar = 100 cents 1 quarter = 25 cents If they add up to $18.50. Therefore 100d + 25q = 1850 Solving two equations we have d + q = 26  equation 1 100d + 25q = 1850  equation 2 d + q = 26 q = 26  d substituting q in equation 2 100d + 25(26  d) = 1850 100d + 650  25d = 1850 75d = 1850  650 75d = 1200 d = 1200/75 = 16 q = 26  d = 26  16 = 10 Jill has 16 dollar coins and 10 quarter coins in her purse. Example: There are 33 coins. They are nickels, dimes and quarters. They total to a value of $3.30. If there are three times as many nickels as quarters, and onehalf as many dimes as nickels. How many coins of each kind are there? Solution: Let 'n' stand for number of nickels, 'd' stand for number of dimes and 'q' for the number of quarters. Then n + d + q = 33 n = 3q d = 0.5n = 0.5(3q) = 1.5q substituting n and d in the equation n + d + q = 33 3q + 1.5q + q = 33 5.5q = 33 q = 6 n = 3q = 3 x 6 = 18 d = 1.5q = 1.5 x 6 = 9 There are 6 quarters 18 nickles and 9 dimes. Example: A box contain the same number of pennies, nickels and dimes. The coins total $1.44. How many of each type of coin does the box contain? Solution: Let 'p' stand for number of pennies, 'n' stand for number of nickles and 'd' stand for number of dimes. There are equal number of each of these implies that number of pennies is p, number of nickles is p and number of dimes is p The value of the coin is the number of cents for each coin times the number of that type of coin, therefore value of pennies = 1p value of nickles = 5p value of dimes = 10p The total value is $1.44 Therefore 1p + 5p + 10p = 144 16p = 144 p = 9 q = 9 d = 9 There are 9 of each type of coin in the box. Directions: Solve the following word problems. 