Chapter 4, Problem 13MCQ

To determine

To determine the greatest number of teams that can be formed from a soccer league of 180 members which consists of 24 eight-year-olds, 96 nine-year-olds, and 60 ten-year-olds

Answer to Problem 13MCQ

12 teams can be formed with 5 members from the 10-year old team

Explanation of Solution

Given information:

A soccer league of 180 members with-

8-year olds=24 members

9-year olds=96 members

10-year olds=60 members

Formula Used- Greatest Common Factor

Calculation- To identify the greatest number of teams possible which have the same number of 8,9 and 10 year olds, find the greatest common factor of 24, 96 & 60.

To find the Greatest Common Factor of these, have to break it down into its factors-

For 24,

  $24=2\times 3\times 2\times 2$

For 60,

  $60=2\times 2\times 3\times 5$

For 96,

  $96=2\times 2\times 3\times 2\times 2$

As visible, $2\times 2\times 3$ is common in all three numbers, hence 12 is the greatest common factor.

Thus, the greatest number of teams possible which have the same number of 8,9 and 10 year olds is 12.

To find the number of members from 10 year old group-

  $\begin{array}{l}\\ \frac{60}{12}=5\end{array}$

Hence, 5 members from the 10 year olds.

Conclusion-

12 teams can be formed with 5 members from the 10-year old team