Question: 30 + .8x = 14 + 1.20x
20 = x + .4
x = 2x ten
b. Solution. .089
3. Joycie has a VIP membership to a movie
theater which costs $27 a year and $6.00 for
each movie she sees. Claire doesnt have a
membership, so she pays $8.25 for each movie
she sees. How many movies would the two girls
have to see in a year in order to pay the same
amount?
a. Equation __________________________
b. Solution __________________________
Graph shapes: a film reel icon is shown in the lower-left area; position_hint=bottom-left.User: Solve
1. **State the problem:**
Joycie pays a yearly membership fee plus a cost per movie, while Claire pays only per movie. We want to find the number of movies $x$ where their total costs are equal.
2. **Define variables and write the equation:**
Let $x$ be the number of movies seen in a year.
Joycie's cost: $$27 + 6x$$
Claire's cost: $$8.25x$$
Set them equal to find $x$:
$$27 + 6x = 8.25x$$
3. **Solve the equation:**
Subtract $6x$ from both sides:
$$27 + \cancel{6x} = 8.25x - \cancel{6x}$$
$$27 = 2.25x$$
Divide both sides by $2.25$:
$$\frac{27}{\cancel{2.25}} = \frac{2.25x}{\cancel{2.25}}$$
$$12 = x$$
4. **Interpretation:**
They must each see $12$ movies in a year to pay the same amount.
**Final answer:**
$$x = 12$$