Cory has a collection of nickels, dime and quarters with a total value of 2.55. There are 6 more dimes than nickels and twice as many quarters as nickels. How many of each coin is in her collection?
just put the words into math:
5n+10d+25q = 255
d = n+6
q = 2n
now just solve for the values.
To solve this problem, we can use algebraic equations. Let's denote the number of nickels as "x".
Given that there are 6 more dimes than nickels, we can write the equation for the number of dimes as: x + 6.
Since there are twice as many quarters as nickels, the equation for the number of quarters becomes: 2x.
Now, we can focus on the values of the coins. The value of a nickel is $0.05, the value of a dime is $0.10, and the value of a quarter is $0.25.
We know that Cory's collection has a total value of $2.55. To represent this, we can create an equation using the values of the coins and their respective quantities:
0.05x + 0.10(x + 6) + 0.25(2x) = 2.55
Now, let's simplify the equation and solve for x:
0.05x + 0.10x + 0.60 + 0.50x = 2.55
0.65x + 0.60 = 2.55
0.65x = 2.55 - 0.60
0.65x = 1.95
x = 1.95 / 0.65
x = 3
Therefore, there are 3 nickels in Cory's collection.
To find the number of dimes, we can substitute the value of x into the equation x + 6:
3 + 6 = 9
So, Cory has 9 dimes.
To find the number of quarters, we can substitute the value of x into the equation 2x:
2 * 3 = 6
Therefore, Cory has 6 quarters.
In conclusion, Cory has 3 nickels, 9 dimes, and 6 quarters in her collection.