Question 24
If Diego has 12 nickels and dimes in his pocket, and they have a combined value of 85 cents, how many of each coin does he have?
dimes

Step 1 ：Let's denote the number of nickels as \(n\) and the number of dimes as \(d\).

Step 2 ：We know that the total number of coins is 12, so we can write this as an equation: \(n + d = 12\).

Step 3 ：We also know that the total value of the coins is 85 cents. Since a nickel is worth 5 cents and a dime is worth 10 cents, we can write this as another equation: \(5n + 10d = 85\).

Step 4 ：We can solve this system of equations to find the values of \(n\) and \(d\).

Step 5 ：The solution to the system of equations is \(d = 5\) and \(n = 7\).

Step 6 ：This means that Diego has 5 dimes and 7 nickels.

Step 7 ：Final Answer: Diego has \(\boxed{5}\) dimes and \(\boxed{7}\) nickels.