Final answer:
To solve the problem, set up two equations representing the given information: x + y = 30 for the total number of coins and 5x + 10y = 260 for the total value of the coins. Solve the system of equations using substitution or elimination method to find the number of nickels and dimes.
Step-by-step explanation:
To solve this problem, we can set up two equations to represent the given information.
Let x be the number of nickels and y be the number of dimes.
From the problem, we know that:
- The total number of coins is 30: x + y = 30
- The total value of the coins is $2.60: 5x + 10y = 260 (since a nickel is worth 5 cents and a dime is worth 10 cents)
We now have a system of two equations. We can solve this system by either substitution or elimination method.
Substitution Method:
- Solve one equation for one variable (e.g., x = 30 - y)
- Substitute this expression into the other equation
- Solve the resulting equation for the other variable (e.g., 5(30 - y) + 10y = 260)
- Solve for y, and then substitute the obtained value of y into one of the original equations to solve for x.
Elimination Method:
- Multiply one equation by a constant so that the coefficients of one variable are the same in both equations
- Add or subtract the equations to eliminate one variable
- Solve the resulting equation for the remaining variable
- Substitute this value into one of the original equations to solve for the other variable.
By solving the system of equations, we can determine the number of nickels and dimes.