Question

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E Math BB Unit 4 Study&Guide
9. The theater has two ways you can watch movies. The first option is to pay $12 per ticket. The second option is to pay $24 per month and $6 per visit. Write and solve an equation to show the number of visits it would take for the cost of the two plans to be equal.
A. 12х = 24 + 6x; 7 = 4
B. 12 = 24 + 6x; x = -2
C. 12x = 24 + 6x; x =2
D. 12x = 24 - 6x: x = 1.33

Answer 1

To determine the number of visits (x) at which the cost of the two options is equal, we can set up an equation based on the costs of each option.

1. The cost of the first option (pay $12 per ticket) for x visits is:
\[
\text{Cost}_1 = 12x
\]

2. The cost of the second option (pay $24 per month and $6 per visit) for x visits is:
\[
\text{Cost}_2 = 24 + 6x
\]

To find the number of visits where these costs are equal, we set the two cost equations equal to each other:
\[
12x = 24 + 6x
\]

Now, we can solve this equation:

1. Subtract \(6x\) from both sides:
\[
12x - 6x = 24
\]
\[
6x = 24
\]

2. Divide by 6:
\[
x = 4
\]

Thus, the cost of the two plans will be equal after 4 visits.

Now let's analyze the answer choices provided:

A. \(12x = 24 + 6x; x = 4\)
B. \(12 = 24 + 6x; x = -2\)
C. \(12x = 24 + 6x; x = 2\)
D. \(12x = 24 - 6x; x = 1.33\)

Given our solved equation (which matches the format in choice A), the correct equation and solution is:

**A. \(12x = 24 + 6x; x = 4\)**