Question

Two-sevenths of the students in the theater club will be in the second show, and three-fifths of them will be in the third show. The rest will be in the first show. If there are 70 students in the theater club, how many of them will be in the first show?

Answer 1

After calculating two-sevenths and three-fifths of the theater club members for the second and third shows respectively, we determine that 8 students from a total of 70 will be in the first show.

Step-by-step explanation:

The question asks us to determine how many students from the theater club will be in the first show. Given that there are 70 students in total in the club, we use fractions to determine the number of students in the second and third shows. Two-sevenths of the students will be in the second show, and three-fifths will be in the third show. Here's how we calculate that:

• To find out how many are in the second show:
  (2/7) × 70 = 20 students.
• To find out how many are in the third show:
  (3/5) × 70 = 42 students.
• To find out how many are in the first show:
  Take the total number of students 70 and subtract the sum of students in the second and third shows (20 + 42 = 62). Therefore, 70 - 62 = 8 students will be in the first show.

So, 8 students will be in the first show.

Answer 2

8 students

Step-by-step explanation:

Let's say there are x students in the theater club. We can set up the following equations to represent the information given in the problem:

• 2/7 * x = number of students in the second show

• 3/5 * x = number of students in the third show

• x - (2/7 * x + 3/5 * x) = number of students in the first show

We are told that there are 70 students in the theater club, so we can substitute 70 for x in the equations above to find the number of students in each show:

• 2/7 * 70 = 20 students in the second show

• 3/5 * 70 = 42 students in the third show

• 70 - (2/7 * 70 + 3/5 * 70) = 8 students in the first show

Therefore, there will be 8 students in the first show.