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.