Problema Solution
A collection of 33 coins, consisting of nickels, dimes, and quarters, has a value of $3.30. If there are three times as many nickels as quarters, and one-half as many dimes as nickels, how many of each coin are there.
Answer provided by our tutors
1 nickle = 5 cents
1 dime = 10 cents
1 quarter = 25 cents
let
n = the number of nickles
d = the number of dimes
q = the number of quarters
A collection of 33 coins, consisting of nickels, dimes, and quarters, has a value of $3.30 = 330 cents
n + d + q = 33
5n + 10d + 25q = 330
if there are three times as many nickels as quarters
n = 3q
and one-half as many dimes as nickels
d = (1/2)n
by solving the system of equations
5n + 10d + 25q = 330
n = 3q
d = (1/2)n
we find
n = 9 nickles
d = 18 dimes
q = 6 quarters
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