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.
number of nickels ----x+2
pennies --------- 3x
10x + 5(x+2) + 1(3x) = 64
solve for x, then sub into my definitions.
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.
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.