Robert has 26 coins that are all nickels and dimes. The value of the coins is $1.85. Write and solve a system of equations thatrepresents this situation.

To solve this problem, we need to set up a system of equations based on the given information. Let's represent the number of nickels as 'N' and the number of dimes as 'D'.

1) First Equation: The total number of coins is 26. Therefore:

N + D = 26

2) Second Equation: The total value of the coins is $1.85. The value of a nickel is $0.05, and the value of a dime is $0.10. So, the equation becomes:

0.05N + 0.10D = 1.85

Now, we have a system of equations:

N + D = 26
0.05N + 0.10D = 1.85

To solve this system, there are multiple methods such as substitution, elimination, or graphical methods. In this case, let's use the substitution method.

From Equation 1, we can express 'N' in terms of 'D':

N = 26 - D

Substituting this value of 'N' into Equation 2:

0.05(26 - D) + 0.10D = 1.85

Simplifying the equation:

1.30 - 0.05D + 0.10D = 1.85

Combine like terms:

0.05D = 1.85 - 1.30
0.05D = 0.55

Divide both sides by 0.05 to solve for 'D':

D = 0.55 / 0.05
D = 11

Now, substitute the value of 'D' back into Equation 1 to solve for 'N':

N + 11 = 26
N = 26 - 11
N = 15

Therefore, the solution to the system of equations is N = 15 and D = 11. This means there are 15 nickels and 11 dimes in Robert's 26 coins.

n+d=26

5n+10d=185