In a collection of nickels, dimes and quarters, there are twice as many dimes as nickels, and 4 fewer quarters than dimes. The total value of the coins is $5.75.
How many nickels are there in the collection ?
30
To find the number of nickels in the collection, let's break down the problem step by step:
1. Start by defining the variables:
Let's assume the number of nickels as "n."
Since there are twice as many dimes as nickels, the number of dimes can be represented as "2n."
And since there are 4 fewer quarters than dimes, the number of quarters can be represented as "2n - 4."
2. Calculate the value of each coin:
The value of a nickel is $0.05.
The value of a dime is $0.10.
The value of a quarter is $0.25.
3. Write an equation to represent the total value of the coins:
Multiply the number of each coin by its value and sum them up:
(0.05n) + (0.10 * 2n) + (0.25 * (2n-4)) = 5.75
4. Solve the equation:
Distribute and simplify the equation:
0.05n + 0.20n + 0.50n - 1.00 = 5.75
0.75n - 1.00 = 5.75
0.75n = 6.75
n = 6.75 / 0.75
n = 9
Therefore, there are 9 nickels in the collection.