Question

Sylvia has all dimes and nickels, totaling up to 20 coins. The total value of the coins is $1.35. Let's assume n = nickles, and d = dimes. What equation can be used to solve the value?

Answer 1

My bad, I meant to say: what equation(s) can we use to find the number of each coin?

Answer 2

Thank you for the answer, but we don't need it right now. I simply need the equations only.

Answer 3

To solve the problem, we can set up two equations based on the information given about the coins.

1. **Total number of coins**: Since Sylvia has a total of 20 coins made up of dimes and nickels,
\[
n + d = 20
\]
where \( n \) is the number of nickels and \( d \) is the number of dimes.

2. **Total value of the coins**: The total value of the coins is $1.35. The value of a nickel is $0.05 and the value of a dime is $0.10. Thus, the total value can be expressed as:
\[
0.05n + 0.10d = 1.35
\]

Now, you can use these two equations to find the values of \( n \) and \( d \).

You could also multiply the second equation by 100 to eliminate the decimals:
\[
5n + 10d = 135
\]

Now, you have the following system of equations to solve:
1. \( n + d = 20 \)
2. \( 5n + 10d = 135 \)

You can now solve this system of equations for the values of \( n \) and \( d \).

Answer 4

No problem! To find the number of each coin (nickels and dimes), we can set up the following equations based on the given conditions:

Let:
- \( n \) = number of nickels
- \( d \) = number of dimes

1. **Equation for the total number of coins**:
\[
n + d = 20
\]
This equation states that the total number of coins (nickels plus dimes) is 20.

2. **Equation for the total value of the coins**:
Since nickels are worth $0.05 each and dimes are worth $0.10 each, the total value of the coins can be represented as:
\[
0.05n + 0.10d = 1.35
\]
To make calculations simpler, you can multiply this equation by 100 to get rid of the decimals:
\[
5n + 10d = 135
\]

Now you have a system of equations to work with:
1. \( n + d = 20 \)
2. \( 5n + 10d = 135 \)

### Solving the equations
You can solve these equations using substitution or elimination.

**Substitution Method**:
1. From the first equation, solve for \( d \):
\[
d = 20 - n
\]

2. Substitute \( d \) into the second equation:
\[
5n + 10(20 - n) = 135
\]
Simplify:
\[
5n + 200 - 10n = 135
\]
Combine like terms:
\[
-5n + 200 = 135
\]
Subtract 200 from both sides:
\[
-5n = -65
\]
Divide by -5:
\[
n = 13
\]

3. Now substitute \( n = 13 \) back into the first equation to find \( d \):
\[
d = 20 - 13 = 7
\]

### Conclusion
Thus, Sylvia has 13 nickels and 7 dimes.

Answer 5

Of course! Here are the equations you need:

1. **Total number of coins**:
\[
n + d = 20
\]

2. **Total value of the coins**:
\[
0.05n + 0.10d = 1.35
\]

Alternatively, you can multiply the second equation by 100 to eliminate decimals:
\[
5n + 10d = 135
\]

These are the equations you can use to find the number of each coin.