EXAMPLE:A person has 3 times as many dimes as he has nickels and 5
more pennies than nickels. If the total amount of these coins is $1.13, how
many of each kind of coin does he have?
SOLUTION:
GOAL: You are being asked to find the number of nickels, pennies, and
dimes.
STRATEGY: Letx¼the number of nickels, 3x¼the number of dimes, and
xþ 5 ¼the number of pennies. Then the value of the nickels is 5x. The value
of the dimes is 10 3 xor 30x. The value of the pennies is 1(xþ5). The total
amount is $1.13100 or 113c. The equation is 5xþ 30 xþ(xþ5)¼113.
IMPLEMENTATION: Solve the equation:
5 xþ 30 xþðxþ 5 Þ¼ 113
5 xþ 30 xþxþ 5 ¼ 113
36 xþ 5 ¼ 113
36 xþ 5 5 ¼ 113 5
36 x¼ 108
361 x
361
¼
108
36
x¼3 (nickels)
3 x¼ 3 3 ¼9 (dimes)
xþ 5 ¼ 3 þ 5 ¼8 (pennies)
There are 3 nickels, 9 dimes, and 8 pennies.
EVALUATION: The value of 3 nickels, 9 dimes, and 8 pennies is
3 5 cþ 9 10 cþ 8 1 c¼ 15 cþ 90 cþ 8 c¼ 113 c or $1.13.
Other types of problems involving values can be solved using the same
strategy as the coin problems. Consider the next example.
110 LESSON 11 Solving Coin Problems