write an equation to solve each problem

There is only one freshman in the cast of the high school musical. There are 6 sophomore and 11 juniors. One third of the cast are seniors. How may seniors are in the musical?
*Please show me the work on how to do it

1+6+11 = 18 = 2/3 of cast

so
cast = 27
27 - 18 = 9
which is indeed 1/3 of the cast

Let's denote the number of seniors in the musical as "x."

According to the problem, there is only one freshman, 6 sophomores, 11 juniors, and one-third of the cast are seniors.

So, the total number of students in the cast is:
1 freshman + 6 sophomores + 11 juniors + x seniors

Since one-third of the cast are seniors, we can write the equation as:
1 freshman + 6 sophomores + 11 juniors + x seniors = (1/3)(1 freshman + 6 sophomores + 11 juniors + x seniors)

Simplifying the equation, we get:
1 + 6 + 11 + x = (1/3)(1 + 6 + 11 + x)

Combining like terms, we have:
18 + x = (1/3)(18 + x)

To solve for x, we can multiply both sides of the equation by 3 to eliminate the fraction:
3(18 + x) = 18 + x

Expanding the equation, we have:
54 + 3x = 18 + x

Next, we can simplify by subtracting x from both sides:
3x - x = 18 - 54

Thus, we get:
2x = -36

Finally, dividing both sides by 2, we find:
x = -18

Therefore, there are -18 seniors in the high school musical. However, since the number of students cannot be negative, it implies that there are no seniors in the musical.

To solve this problem, we need to set up an equation. Let's let "x" represent the number of seniors in the musical.

First, we are told that there is only one freshman, 6 sophomores, and 11 juniors. So, the number of students in the cast can be calculated as follows:

Number of students = 1 (freshman) + 6 (sophomores) + 11 (juniors) + x (seniors).

We are also given that one third of the cast are seniors. In other words, the number of seniors is one-third of the total number of students. This can be expressed mathematically as:

x = (1/3) * (total number of students)

Now, substitute the total number of students in terms of freshman, sophomores, juniors, and seniors:

x = (1/3) * (1 + 6 + 11 + x)

To solve for x, we can multiply both sides of the equation by 3 to eliminate the fraction:

3x = 1 + 6 + 11 + x

Simplifying the right side of the equation:

3x = 18 + x

Next, we want to isolate the variable x on one side of the equation. To do this, we can subtract x from both sides:

3x - x = 18

Simplifying the left side of the equation:

2x = 18

Finally, divide both sides of the equation by 2 to solve for x:

x = 18/2

x = 9

Therefore, there are 9 seniors in the high school musical.