If I have 27 coins (dimes and nickels) that total $1.95. How many are dimes and how many are nickels
D = # of Dimes, N = # of nickels
D + N = 27, therefore
D = 27 - N
.10D + .05N = 1.95
Substitute 27 - N for D in second equation and solve for N. Put that value in the first equation to find D. To check, put both in the second equation.
I hope this helps.
To solve this problem, let's set up a system of equations.
Let's say we have x dimes and y nickels.
Since the total number of coins is 27, we can express this as an equation:
x + y = 27
Next, let's look at the value of the coins. Each dime is worth 10 cents, so the total value of the dimes is 10x cents. Similarly, each nickel is worth 5 cents, so the total value of the nickels is 5y cents.
Since the total value of the coins is $1.95, we can express this as a second equation:
10x + 5y = 195 (converted the dollars to cents)
Now, we have a system of equations:
x + y = 27 (equation 1)
10x + 5y = 195 (equation 2)
We can solve this system of equations to find the values of x (number of dimes) and y (number of nickels).
One method to solve this system is substitution. Solve equation 1 for x:
x = 27 - y
Substitute this value of x into equation 2:
10(27 - y) + 5y = 195
Now, simplify and solve for y:
270 - 10y + 5y = 195
-5y = -75
y = 15
Now that we have the value of y, we can substitute it back into equation 1 to find x:
x + 15 = 27
x = 12
Therefore, there are 12 dimes and 15 nickels.