Question

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**