Carter has 37!'98!$ 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 \( n \) be the number of nickels and \( d \) be the number of dimes. We know that:

1. The total number of coins is given by the equation: \[ n + d = 37 \]

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

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

Now, we have the system of equations:

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

We can solve for \( n \) in the first equation: \[ n = 37 - d \]

Substituting this expression for \( n \) into the second equation: \[ (37 - d) + 2d = 62 \] This simplifies to: \[ 37 + d = 62 \] Thus: \[ d = 62 - 37 = 25 \]

Now substituting back to find \( n \): \[ n = 37 - d = 37 - 25 = 12 \]

So, the solution is:

• Number of nickels (\( n \)): 12
• Number of dimes (\( d \)): 25

To confirm, we check the calculations:

• Total number of coins: \( 12 + 25 = 37 \)
• Total value: \( 5 \cdot 12 + 10 \cdot 25 = 60 + 250 = 310 \) cents, which is indeed $3.10.

Thus, Carter has 12 nickels and 25 dimes.