Question

There are 75 coins in a piggy bank all of which are either nickels or dimes. If the value of all the coins combined is $6.05, then how many nickels and dimes are there?

Answer 1

By setting up a system of equations and solving for variables representing the number of nickels and dimes, it's determined that there are 29 nickels and 46 dimes in the piggy bank.

Step-by-step explanation:

A student needs to determine how many nickels and dimes are in their piggy bank, where the total count of coins is 75 and their combined value is $6.05. To solve this, we can set up a system of equations based on the following facts: each nickel is worth 5 cents (or $0.05) and each dime is worth 10 cents (or $0.10). Let's use 'n' to represent the number of nickels and 'd' to represent the number of dimes.

• The total number of coins is 75: n + d = 75
• The total value of coins is $6.05: 0.05n + 0.10d = 6.05

By solving this system of equations, we can find the values of 'n' and 'd' that satisfy both conditions. Multiplying the second equation by 100 to get rid of decimals, we get:

5n + 10d = 605

Now let's multiply our first equation by 5:

5n + 5d = 375

Subtracting this from the modified second equation:

(5n + 10d) - (5n + 5d) = 605 - 375

Which simplifies to:

5d = 230

Dividing by 5:

d = 46

So there are 46 dimes. Plugging this value into our first equation to find 'n':

n + 46 = 75

n = 75 - 46

n = 29

There are 29 nickels and 46 dimes in the piggy bank.