Question

There are 4 times as many nickels as dimes in a coin bank. The coins have a total value of 600 cents (6.00 dollar) Find the number of nickels.

Short answer

The number of nickels in the coin bank is 80.

Step-by-step solution

Define the variables

Let the number of dimes be represented as \( d \). Given the relationship between the number of nickels and dimes, the number of nickels can be represented as \( 4d \).

Set up the equation

The total value of the coins is 600 cents or 6 dollars. Recognizing that a dime is 10 cents and a nickel is 5 cents, the equation can be set up as follows: \( 5(4d) + 10d = 600\), which simplifies to \( 30d = 600\).

Solve the equation

To solve for \( d \), one can divide each side of the equation by 30. This leads to \( d = 20 \).

Find the number of nickels

Substituting \( d = 20 \) into the equation for the number of nickels yields \( 4d = 4*20 = 80 \). Thus, there are 80 nickels in the coin bank.