Martin has a combination of 33 quarters and dimes worth a total of [tex]\(\$6\)[/tex]. Which system of linear equations can be used to find the number of quarters, [tex]\(q\)[/tex], and the number of dimes, [tex]\(d\)[/tex], Martin has?
A. [tex]\[
\begin{array}{l}
q + d = 6 \\
25q + 10d = 33
\end{array}
\][/tex]
B. [tex]\[
\begin{array}{l}
q + d = 6 \\
0.25q + 0.1d = 33
\end{array}
\][/tex]
C. [tex]\[
q + d = 33 \\
25q + 10d = 6
\][/tex]
D. [tex]\[
\begin{array}{l}
q + d = 33 \\
0.25q + 0.1d = 6
\end{array}
\][/tex]
To solve this problem, we need to create a system of linear equations based on the information provided:
1. Martin has a total of 33 quarters and dimes. This can be expressed as: [tex]\[
q + d = 33
\][/tex] where [tex]\( q \)[/tex] represents the number of quarters and [tex]\( d \)[/tex] represents the number of dimes.
2. The total value of these quarters and dimes is [tex]$\$[/tex]6[tex]$. Since one quarter is worth \$[/tex]0.25 and one dime is worth \$0.10, the value equation can be written as: [tex]\[
0.25q + 0.1d = 6
\][/tex]
Therefore, the system of linear equations that can be used to find the number of quarters [tex]\( q \)[/tex] and the number of dimes [tex]\( d \)[/tex] is: [tex]\[
\begin{cases}
q + d = 33 \\
0.25q + 0.1d = 6
\end{cases}
\][/tex]
Hence, the correct system of linear equations is: [tex]\[
\begin{array}{l}
q + d = 33 \\
0.25 q + 0.1 d = 6
\end{array}
\][/tex]
