Question

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**.