1. A collection of 52 dimes and nickels is worth $4.50. How many nickels are there?
14 nickels
D = 52 - N
10D + 5N = 10(52-N) + 5N = $4.50
Solve for N.
To solve this problem, we can create a system of equations based on the given information. Let's represent the number of dimes as 'D' and the number of nickels as 'N'.
We know that there are a total of 52 dimes and nickels, so we can write the equation:
D + N = 52 -- Equation 1
We also know that the total value of all the coins is $4.50. The value of a dime is 10 cents and a nickel is 5 cents, so we can write another equation to represent the total value:
10D + 5N = 450 -- Equation 2
Now, we have a system of two equations with two variables. We can solve this system to find the values of D and N.
We can use the method of substitution or elimination to solve the system. Let's use substitution method:
From Equation 1, we can rewrite it as D = 52 - N.
Substitute this expression for D in Equation 2:
10(52 - N) + 5N = 450
520 - 10N + 5N = 450
520 - 5N = 450
-5N = 450 - 520
-5N = -70
To solve for N, divide both sides of the equation by -5:
N = -70 / -5
N = 14
Therefore, there are 14 nickels in the collection.