there are some nickels and dimes in a jar. the number of nickels is one less than twice the number of dimes.if the total value of coins is 8 dollars and 55 cents, then find the numbers of dimes?
explain?
n = 2d-1
5n+10d = 855
now crunch the numbers.
To find the number of dimes, we need to set up a system of equations based on the given information. Let's define:
- x as the number of dimes in the jar
- y as the number of nickels in the jar
We know that the number of nickels is one less than twice the number of dimes, so we can write the equation:
y = 2x - 1 -- Equation 1
We also know that the total value of the coins is $8.55. A dime is worth 10 cents and a nickel is worth 5 cents, so we can set up the equation:
10x + 5y = 855 -- Equation 2
Now we have a system of equations with Equation 1 and Equation 2. We can solve this system to find the values of x and y, which represent the number of dimes and nickels, respectively.
1. Start by substituting Equation 1 into Equation 2:
10x + 5(2x - 1) = 855
2. Distribute the 5:
10x + 10x - 5 = 855
3. Combine like terms:
20x - 5 = 855
4. Add 5 to both sides:
20x = 860
5. Divide both sides by 20:
x = 43
Therefore, the number of dimes is 43.