Question

Patrick has nickels and dimes in his piggy bank. If he has $2.10 and 30 coins in his bank, how many of each coin does he have?

a) 12 nickels, 18 dimes
b) 14 nickels, 16 dimes
c) 16 nickels, 14 dimes
d) 18 nickels, 12 dimes

Answer 1

By creating a system of equations from the given information about the total value and number of coins and solving it, we find that Patrick has 18 nickels and 12 dimes in his piggy bank.

Step-by-step explanation:

The question asks us to determine how many nickels and dimes Patrick has in his piggy bank, given that he has $2.10 and 30 coins in total. Let's denote nickels by n and dimes by d. We have two pieces of information that can be turned into equations:

• The total value of the coins is $2.10, which can be written as 5n + 10d = 210 cents (since 1 nickel is worth 5 cents and 1 dime is worth 10 cents).
• The total number of coins is 30, which can be written as n + d = 30.

We can solve this system of equations using substitution or elimination. First, we simplify the first equation by dividing all terms by 5, giving us n + 2d = 42. Now we have two equations:

1. n + d = 30
2. n + 2d = 42

Subtracting the first equation from the second gives us d = 12. Substituting d = 12 into the first equation yields n = 18. Thus, Patrick has 18 nickels and 12 dimes.