Carter has 37 coins all nickels and dimes in his piggy bank the value of the coins is $3.10. How many each kind of coin is there?

Answer 1

Let's use a system of equations to solve the problem.

Let:

• \( n \) = number of nickels
• \( d \) = number of dimes

From the problem, we have the following two equations:

1. The total number of coins: \[ n + d = 37 \]

2. The total value of the coins in cents (since $3.10 is 310 cents): \[ 5n + 10d = 310 \]

Now, we can simplify the second equation by dividing everything by 5: \[ n + 2d = 62 \]

Now we have a system of two equations:

1. \( n + d = 37 \)
2. \( n + 2d = 62 \)

We can solve for \( n \) by subtracting the first equation from the second equation: \[ (n + 2d) - (n + d) = 62 - 37 \] This simplifies to: \[ d = 25 \]

Now, we can substitute \( d \) back into the first equation to find \( n \): \[ n + 25 = 37 \] Subtracting 25 from both sides gives: \[ n = 12 \]

So, Carter has:

• 12 nickels
• 25 dimes

To summarize:

• Number of nickels: 12
• Number of dimes: 25