Diane has $1.20 in dimes and nickels. She has a total of 13 coins. How many of each kind does she have?
add up the coins:
n+d = 13
add up the values:
5n+10d = 120
Now just solve for n and d.
2 N
11D ?
well, geez, just check your answer
11 dimes and 2 nickels does indeed add up to $1.20
To find out how many dimes and nickels Diane has, we can set up a system of equations:
Let's assume the number of dimes Diane has is represented by "D" and the number of nickels she has is represented by "N".
From the given information, we can create two equations:
1. The total value equation: The value of the dimes plus the value of the nickels equals $1.20.
This can be expressed as:
0.10D + 0.05N = 1.20
2. The total number of coins equation: The number of dimes plus the number of nickels equals 13.
This can be expressed as:
D + N = 13
Now, we have a system of two linear equations:
Equation 1: 0.10D + 0.05N = 1.20
Equation 2: D + N = 13
We can solve this system of equations using substitution or elimination methods. For this example, let's use the elimination method.
First, let's multiply each term of Equation 1 by 100 to eliminate the decimal points:
10D + 5N = 120
D + N = 13
Next, we'll multiply all terms of the second equation by -10:
-10D - 10N = -130
Now, we can add the two equations together:
(10D + 5N) + (-10D - 10N) = 120 + (-130)
This simplifies to:
-5N = -10
Divide both sides of the equation by -5:
N = 2
Now that we know N (the number of nickels), we can plug it back into Equation 2 to find D (the number of dimes):
D + 2 = 13
D = 13 - 2
D = 11
So, Diane has 11 dimes and 2 nickels.