\begin{tabular}{l} 3. A group of adults plus one child attend a movie at \ Cineplex 15 . Tickets cost $$ \$ 9 $$ for adults and $$ \$ 6 $$ for \ children. The total cost for the movie is $$ \$ 78 $$. Write an \ equation to find the number of adults in the group. \ Variable: \ Coefficient: \ Constants: \ \hline Equation: \end{tabular}

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Sure, let's break down the problem step by step by identifying the variable, coefficient, constants, and then forming the equation.

$$
\begin{array}{|l|l|}
\hline
\textbf{Component} & \textbf{Details} \
\hline
\text{Variable} & \text{Let } a \text{ represent the number of adults in the group.} \
\hline
\text{Coefficient} & 9 \text{ (price per adult ticket)} \
\hline
\text{Constants} & 6 \text{ (price for one child ticket)} \
& 78 \text{ (total cost)} \
\hline
\text{Equation} & 9a + 6 = 78 \
\hline
\end{array}
$$

**Explanation:**

1. **Variable:** We let $$ a $$ represent the number of adults.
2. **Coefficient:** Each adult ticket costs \$9, so the coefficient of $$ a $$ is 9.
3. **Constants:** There's one child in the group, and the child ticket costs \$6. The total cost is \$78.
4. **Equation:** The total cost is the sum of the cost of adult tickets and the child ticket:
   $$
   9a + 6 = 78
   $$

You can solve the equation for $$ a $$ to find the number of adults:

$$
9a + 6 = 78 \
9a = 78 - 6 \
9a = 72 \
a = \frac{72}{9} \
a = 8
$$

So, there are **8 adults** in the group.
Let $$ a $$ be the number of adults. The equation is $$ 9a + 6 = 78 $$.

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