In counting the money collected on his paper route Frank finds that he has 3 more dimes than nickles and 3 less dimes than quarters. If his total collections amounted to $13.40, how many coins of each kind did he have?

Elementary Algebra
17th Edition
ISBN:9780998625713
Author:Lynn Marecek, MaryAnne Anthony-Smith
Publisher:Lynn Marecek, MaryAnne Anthony-Smith
Chapter3: Math Models
Section3.3: Solve Mixture Applications
Problem 3.52TI: Liliana has $2.10 in nickels and quarters in her backpack. She has 12 more nickels than quarters....
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In counting the money collected on his paper route Frank finds that he has 3 more dimes than nickles and 3 less dimes than quarters. If his total collections amounted to $13.40, how many coins of each kind did he have?

Expert Solution
Step 1

There are 3 more dimes than nickels and 3 less dimes than quarters. The total collection amounts to $13.40.

Let the number of dimes be D, the number of nickels be N and the number of quarters be
Q.
According to given, 3 more dimes than nickel means the number ofnickels are 3 less
than the number of dimes. That is, N = D -3
Three less dimes than quarters means the number of quarters are 3 more than the number
of dimes. That is, Q D+3
Step 2

The total collection is $13.40, that is

5N 10D 25Q= $13.40
Step 3

As 1 nickel is 5 cents, 1 dime is 10 cents, 1 quarter is 25 cents and 1 $ is 100 cents, the collection equation becomes

5N 10D 25Q=1340
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