Chapter 6.5, Problem 47STP

(a)

To determine

To Find:Number ofstudents at Henderson Middle school participate in sports if there are $645$ total students.

Answer to Problem 47STP

  $\frac{100}{258}=\frac{m}{n}$

Explanation of Solution

Given: There are $258$ eight grades at Henderson Middle school. The graph shown below shows how many of the eight grade participate in each sport.

  

If each student participate in only one sport, write a proportion that would be used to predict that how many students at Henderson Middle school participate in sports if there are $645$ total students.

Using the cross product formula

  $\begin{array}{l}\frac{a}{b}=\frac{c}{d}\\ ad=bc\end{array}$

Now

Total eight graders in the sports that take participation

  $25+38+21+7+9=100$

And

Total number of students in eight grade = $258$

Let $m$ be the eight graders who are into sports

Let $n$ be the total population

Then

Proportion is

  $\frac{100}{258}=\frac{m}{n}$

(b)

To determine

To Solve: The proportion in part a.

Answer to Problem 47STP

  $250$ students

Explanation of Solution

Given: There are $258$ eight grades at Henderson Middle school. The graph shown below shows how many of the eight grade participate in each sport.

  

If each student participate in only one sport, write a proportion that would be used to predict that how many students at Henderson Middle school participate in sports if there are $645$ total students.

Proportion is

  $\frac{100}{258}=\frac{m}{n}$

If the number of students of eight grade is $645$

Then

  $\begin{array}{l}\frac{100}{258}=\frac{m}{n}\\ 100n=258m\\ 100(645)=258m\\ m=250\end{array}$

(c)

To determine

To Solve: The proportion that could be used to predict the eighth graders that participate in track if there are $220$ total eighth graders.

Answer to Problem 47STP

  $\frac{25}{258}=\frac{m}{220}$

Explanation of Solution

Given: There are $258$ eight grades at Henderson Middle school. The graph shown below shows how many of the eight grade participate in each sport.

  

Write and solve the proportion that could be used to predict the eighth graders that participate in track if there are $220$ total eighth graders.

Proportion is

  $\frac{100}{258}=\frac{m}{n}$

The number of students in the track is $25$

i.e.

  $a=25$

And number of students of eight grade is $220$

Then

  $\begin{array}{l}\frac{25}{258}=\frac{m}{220}\\ 220(25)=258m\\ 5500=258m\\ m=\frac{5500}{258}\\ m=21.3\end{array}$

Then $m=21.3$