Question

Martin has combo 33 quarters and dimes worth $6. What system of linear equations can find number of quarters and number of dimes

Answer 1

To find the number of quarters and dimes Martin has, we can define two variables:

- Let \( q \) be the number of quarters.
- Let \( d \) be the number of dimes.

We can set up a system of linear equations based on the information provided.

1. The first equation derives from the total number of coins:
\[
q + d = 33
\]
(This expresses that the total number of quarters and dimes is 33.)

2. The second equation comes from the total value of the coins. Since quarters are worth $0.25 and dimes are worth $0.10, we can express the total value in dollars:
\[
0.25q + 0.10d = 6
\]
(This states that the total value of the coins is $6.)

Thus, the system of linear equations is:
\[
\begin{align*}
1) & \quad q + d = 33 \\
2) & \quad 0.25q + 0.10d = 6
\end{align*}
\]

You can solve this system of equations to find the number of quarters (\( q \)) and dimes (\( d \)).