Nadia has 32 coins made up of nickles, dimes, and quarters. The sum of the number of nickels and the number of quarters is three times the number of dimes. If the total value of the coins is $4.60, how many of each kind does she have?
I can't figure out how to make this word problem into 3 equations.
To solve this word problem, we need to translate the given information into a system of equations. Let's start by assigning variables to each unknown quantity:
Let's assume that Nadia has "x" nickels, "y" dimes, and "z" quarters.
From the problem, we are given the following information:
1) The sum of the number of nickels and the number of quarters is three times the number of dimes:
x + z = 3y
2) The total number of coins she has is 32:
x + y + z = 32
3) The total value of the coins is $4.60:
0.05x + 0.10y + 0.25z = 4.60
Now we have our three equations with three variables. By solving this system of equations, we can determine the values for "x", "y", and "z" to find out how many nickels, dimes, and quarters Nadia has.