A collection of coins has a value of 64 cents. There are two more nickels than dimes and three times as many pennies as dimes. How many of each kind of coins are there?
number of dimes ---- x
number of nickels ----x+2
pennies --------- 3x
10x + 5(x+2) + 1(3x) = 64
solve for x, then sub into my definitions.
Let's break down the given information:
Let's assume the number of dimes = D
The number of nickels = D + 2 (two more than dimes)
The number of pennies = 3D (three times as many as dimes)
Now let's calculate the total value of the coins:
Value of dimes = 10D cents
Value of nickels = 5(D + 2) cents
Value of pennies = 1(3D) cents
According to the given information, the total value of the coins is 64 cents:
10D + 5(D + 2) + 1(3D) = 64
Simplifying the equation:
10D + 5D + 10 + 3D = 64
18D + 10 = 64
18D = 54
D = 54 / 18
D = 3
So, there are 3 dimes.
Now, let's calculate the number of nickels and pennies:
Number of nickels = D + 2 = 3 + 2 = 5
Number of pennies = 3D = 3 × 3 = 9
Therefore, there are 3 dimes, 5 nickels, and 9 pennies in the collection.
To solve this problem, we can set up a system of equations based on the given information.
Let's denote:
- Dimes as "x"
- Nickels as "x + 2" (since there are 2 more nickels than dimes)
- Pennies as "3x" (since there are three times as many pennies as dimes)
The value of each coin can be expressed as follows:
- Value of dimes: 10x (since each dime is worth 10 cents)
- Value of nickels: 5(x + 2) (since each nickel is worth 5 cents)
- Value of pennies: 1(3x) (since each penny is worth 1 cent)
Now, we can set up the equation based on the given information about the total value of the coins:
10x + 5(x + 2) + 1(3x) = 64
Simplify and solve the equation:
10x + 5x + 10 + 3x = 64
18x + 10 = 64
18x = 54
x = 3
So, there are 3 dimes, 3 + 2 = 5 nickels, and 3(3) = 9 pennies.