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Let $n$ represent the number of people in the group who are not members of the fan club and $m$ represent the number of members. It is given that there are $11$ people in the group. Using this information, we can write the equation $n+m=11.$ It is also given that a non-member pays $\$18$ for a ticket and a member pays $\$13$ dollars, and that they together pay $\$178$ for their tickets. Using this information, we can write the equation $18n+13n=178.$ Combining these equations we have the following system of equations. $\begin{cases}n+m=11 \\ 18n+13m=178 \end{cases}$

b

$18n+13m=178$

Substitute$n={\color{#0000FF}{11-m}}$

$18({\color{#0000FF}{11-m}})+13m=178$

DistrDistribute $18$

$198-18m+13m=178$

$m=4$

$n+m=11$

Substitute$m={\color{#0000FF}{4}}$

$n+{\color{#0000FF}{4}}=11$

SubEqn$\text{LHS}-4=\text{RHS}-4$

$n=7$