Chapter 3.1, Problem 49PPS

(a)

To determine

To Write: the system of two equation representing number of singles and double matches going on.

Answer to Problem 49PPS

  $x+y=13$ and $4y+2x=38$ .

Explanation of Solution

Given:

Total number of matches going on is $13$

Total number people playing the matches are $38$ .

Double match has $4$ players and single match has $2$ players.

Calculation:

Let $x$ be the number of double matches and $y$ be the number single matches being played.

Equation for total number of matches.

  $x+y=13\mathrm{......}\left(1\right)$ …… (1)

Equation for total number of players using

Numbers of Players $\text{=}$ Number of Matches $\times$ Number of players in each match

  $4y+2x=38\mathrm{.......}\left(2\right)$

Therefore, the system of equations is $x+y=13$ and $4y+2x=38$ .

(b)

To determine

To Find;the number of double and single matches being played.

Answer to Problem 49PPS

Double matches are $6$ and single matches are $7$ .

Explanation of Solution

Given;

Equations are given for number of players and number of matches as.

  $x+y=13$ and $4y+2x=38$ .

Here, $x$ is the number of double matches and $y$ is the number single matches being played.

Calculation;

solving equation $x+y=13$ for y.

  $\begin{array}{l}x+y=13\\ y=13-x\end{array}$

Substituting $y=13-x$ in another equation.

  $\begin{array}{l}4y+2x=38\\ 4\times \left(13-x\right)+2x=38\\ 52-4x+2x=38\\ 52-38=2x\\ 14=2x\\ x=7\end{array}$

Substituting $x=7$ in first equation.

  $\begin{array}{l}x+y=13\\ 7+y=13\\ y=6\end{array}$

Therefore, the number of double matches is $6$ and number of single matches is $7$ .