you have 28 coins that are all nickles and dimes. the value of the coins is $2.05. Find the amount of nickles and dimes that you have.
systems of sub.
of substitution
0.05x + 0.10y = 2.05
x + y = 28
To find the number of nickels and dimes you have, let's use a system of equations.
Let's assume the number of nickels is N and the number of dimes is D.
The first equation we can set up is based on the total number of coins:
N + D = 28 ---(Equation 1)
The second equation is based on the total value of the coins:
0.05N + 0.1D = 2.05 ---(Equation 2)
Now we have a system of equations. We can solve this system using different methods, such as substitution or elimination.
For simplicity, let's solve it using the substitution method. We solve Equation 1 for N:
N = 28 - D
Now substitute this value of N into Equation 2:
0.05(28 - D) + 0.1D = 2.05
Expand and simplify:
1.4 - 0.05D + 0.1D = 2.05
Combine like terms:
0.05D + 0.1D = 2.05 - 1.4
0.15D = 0.65
Divide both sides by 0.15:
D = 0.65 / 0.15
D ≈ 4.33
Since you can't have a fraction of a coin, let's round D to the nearest whole number. So, D = 4.
Now substitute the value of D back into Equation 1:
N + 4 = 28
N = 28 - 4
N = 24
Hence, you have 24 nickels and 4 dimes.