Final answer:
To determine how many nickels and dimes are in a combination of 20 coins with a total value of $1.55, you can set up a system of equations and solve for the variables. In this case, there are 9 nickels and 11 dimes in the combination of 20 coins.
Step-by-step explanation:
To determine how many nickels and dimes are in a combination of 20 coins with a total value of $1.55, we can set up a system of equations.
Let's assume the number of nickels is 'x' and the number of dimes is 'y'.
From the given information, we can create two equations:
- 5x + 10y = 155 (representing the total monetary value in cents)
- x + y = 20 (representing the total number of coins)
We can solve this system of equations using substitution or elimination. Let's use the elimination method:
- Multiply the second equation by 5 to make the coefficients of 'x' in both equations the same: 5x + 5y = 100
- Subtract equation 2 from equation 1 to eliminate 'x': (5x + 10y) - (5x + 5y) = 155 - 100
- Simplify the equation: 5y = 55
- Divide both sides by 5 to solve for 'y': y = 11
- Substitute the value of 'y' into equation 2 to solve for 'x': x + 11 = 20
- Solve for 'x': x = 9
Therefore, there are 9 nickels and 11 dimes in the combination of 20 coins.