There are 47 people attending a play at an outdoor theater. There are 11 groups of people sitting in groups of 3 or 5. How many groups of each size are there?

The number of groups in 3 is 4 groups. The number of groups in 5 is 7 groups.

Step-by-step explanation:

Let the number of groups in 3 ⇒ x

Let the number of groups in 5 ⇒ y

There are 11 groups. ⇒ x + y = 11 → (1)

There are 47 people. ⇒ 3x + 5y = 47 → (2)

Solve (1) and (2) to get x and y.

From (1) ⇒ y = 11 - x → (3)

By substitution from (3) at (2) with y

∴ 3x + 5 (11-x) = 47

3x + 55 - 5x = 47

-2x = 47 - 55 = - 8

∴ x = - 8/-2 = 4

∴ y = 11 - x = 11 - 4 = 7

So, the number of groups in 3 is 4 groups.

the number of groups in 5 is 7 groups.