Item 2 at a park, there are 38 people playing tennis. some are playing doubles (2 teams of 2 people each) and some are playing singles (1 person against 1 person). there are 13 matches in progress. a doubles match requires 4 players, and a singles match requires 2 players. how many matches of each type are in progress?

Number of doubles games = 6

Number of singles games = 7

Step-by-step explanation:

Let the number doubles be d and number of singles be s.

There are 13 matches in progress.

                         d + s = 13  eqn 1

There are 38 people playing tennis. A doubles match requires 4 players, and a singles match requires 2 players.

                    4 d + 2 s = 38  eqn 2

eqn 1 x 2

                         2d + 2s = 26  eqn 3

eqn 2 - eqn 3

                          4 d + 2 s -  2d + 2s = 38 - 26

                             2d = 12

                                d = 6

Substituting in eqn 1

                            6 + s = 13          

                                   s = 7

Number of doubles games = 6

Number of singles games = 7