Chapter 7, Problem 21CP

To determine

To find: The number of games the team win.

Answer to Problem 21CP

The number of games the team win is $21$ .

Explanation of Solution

Given information: The ratio of the number of wins to the total number of games played for a basketball team equals $\stackrel{-}{0.63}$ . The team lost $12$ games. How many games did the team win?

Calculation:

Let, The ration of the number of wins to the number of games played is $x:y$ $\mathrm{......}(1)$

Where, $x:y$ $=$ $\stackrel{-}{0.63}$ , and $\stackrel{-}{0.63}$ can be written as,

  $\begin{array}{l}=\stackrel{-}{0.63}\\ =\frac{\stackrel{-}{63}}{100}\\ =\frac{63}{99}\\ =\frac{7}{11}\\ =7:11\end{array}$

Since, The team lost $12$ games i.e.

  $\begin{array}{l}y-x=12\\ y=12+x\end{array}$

Let’s find the value of $x$ and $y$ from the equation $(1)$ ,

  $\begin{array}{c}x:y=7:11\\ \frac{x}{y}=\frac{7}{11}\\ \frac{x}{12+x}=\frac{7}{11}\\ 11x=84+7x\\ 11x-7x=84\\ 4x=84\\ x=21\end{array}$

Hence, The number of games the team has win is $21$ .

  $\begin{array}{l}=\text{Total number of games}-\text{Number of games the team has lost}\\ \text{=}33-\end{array}$