To find the number of bracelets [tex]\( b \)[/tex] and necklaces [tex]\( n \)[/tex] that Lily sold, we need to set up a system of equations based on the given information.
1. Total Items Sold:
Lily sold 18 items in total. This gives us the first equation:
[tex]\[
b + n = 18
\][/tex]
2. Total Revenue:
She sold bracelets for \[tex]$6 each and necklaces for \$[/tex]5 each for a total of \$101. This gives us the second equation:
[tex]\[
6b + 5n = 101
\][/tex]
So, the correct system of equations that represents the scenario is:
[tex]\[
\begin{cases}
b + n = 18 \\
6b + 5n = 101
\end{cases}
\][/tex]
To solve this system, we can use the substitution or elimination method, but the problem specifically asks which system of equations can be used, and we have found that correct system now. So the correct choice among the given options is:
[tex]\[
\begin{array}{l}
b+n=18 \\
6b+5n=101
\end{array}
\][/tex]
This is the correct system of equations to determine the number of bracelets and necklaces Lily sold.
