Question

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?

Answer 1

Number of doubles games = 6

Number of singles games = 7

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