Cory has a collection of nickles, dines, and quarters with a total value of $3.60. There are 6 more dimes than nickels and twice as many quarters as nickles. How many of each coin is in her collection?
5 n + 10 d + 25 q = 360
d = n + 6
q = 2 n
substituting ... 5 n + 10(n + 6) + 25(2 n) = 360
... 5 n + 10 n + 60 + 50 n = 360
solve for n , then substitute back to find d and q
the numbers do not "work out"
... check for a typo , and proceed with correct values
Why did the coin collection go to therapy? It had too many issues!
Let's solve this riddle. Let's say Cory has x nickels. If there are 6 more dimes than nickels, then she has x + 6 dimes. And if there are twice as many quarters as nickels, then Cory has 2x quarters.
Now, let's calculate the total value of the coins. A nickel is worth $0.05, a dime is worth $0.10, and a quarter is worth $0.25. So, the total value equation is:
0.05x + 0.10(x + 6) + 0.25(2x) = 3.60
Now we can solve for x:
0.05x + 0.10x + 0.60 + 0.50x = 3.60
0.65x + 0.60 = 3.60
0.65x = 3.60 - 0.60
0.65x = 3.00
x = 3.00 / 0.65
x ≈ 4.62
Since we can't have a fraction of a coin, let's round x down to the nearest whole number:
x = 4
So, Cory has 4 nickels. If there are 6 more dimes than nickels, then she has 4 + 6 = 10 dimes. And if there are twice as many quarters as nickels, then she has 2 * 4 = 8 quarters.
Therefore, Cory has 4 nickels, 10 dimes, and 8 quarters in her collection.
Let's start solving the problem step by step.
Step 1: Assign variables to the unknowns.
Let's assume the number of nickels is N, dimes is D, and quarters is Q.
Step 2: Convert the given information into equations.
We are given two pieces of information:
1. The total value of all the coins is $3.60.
The value of 1 nickel is $0.05, 1 dime is $0.10, and 1 quarter is $0.25. So, we can express this information using the following equation:
0.05N + 0.10D + 0.25Q = 3.60
2. There are 6 more dimes than nickels.
This can be expressed as D = N + 6.
Step 3: Use the third given information to form another equation.
Twice the number of nickels is equal to the number of quarters.
This can be expressed as Q = 2N.
Step 4: Now we have a system of equations. Solve them simultaneously.
Using Equation 2, substitute D = N + 6 into Equation 1:
0.05N + 0.10(N + 6) + 0.25(2N) = 3.60
Simplifying the equation:
0.05N + 0.10N + 0.60 + 0.50N = 3.60
0.65N + 0.60 = 3.60
0.65N = 3.60 - 0.60
0.65N = 3.00
Divide both sides of the equation by 0.65:
N = 3.00 / 0.65
N ≈ 4.62
Since the number of coins must be a whole number, let's round N down to 4 (since we can't have a fraction of a coin).
Now we can find the values of D and Q using the equations D = N + 6 and Q = 2N:
D = 4 + 6 = 10
Q = 2(4) = 8
Therefore, Cory has 4 nickels, 10 dimes, and 8 quarters in her collection.
To solve this problem, let's break it down step by step:
1. Let's assume the number of nickels as 'x'.
2. Since there are 6 more dimes than nickels, the number of dimes will be 'x + 6'.
3. Since there are twice as many quarters as nickels, the number of quarters will be '2x'.
4. Now, we can calculate the total value of each coin:
- The value of nickels will be 0.05x (as 1 nickel is equal to $0.05).
- The value of dimes will be 0.10(x + 6) (as 1 dime is equal to $0.10).
- The value of quarters will be 0.25(2x) (as 1 quarter is equal to $0.25).
5. The total value of all coins is $3.60, so we can set up the equation:
0.05x + 0.10(x + 6) + 0.25(2x) = 3.60
Simplifying the equation:
0.05x + 0.10x + 0.60 + 0.50x = 3.60
0.65x + 0.60 = 3.60
0.65x = 3.60 - 0.60
0.65x = 3.00
x = 3.00 / 0.65
x ≈ 4.62
Since we can't have a fraction of a coin, we'll need to round down to the nearest whole number. Therefore, the number of nickels is 4.
6. Now that we have the value of x, we can find the number of dimes and quarters as follows:
- Number of dimes: x + 6 = 4 + 6 = 10
- Number of quarters: 2x = 2 * 4 = 8
So, Cory has 4 nickels, 10 dimes, and 8 quarters in her collection.