Q12. - Algebra 2

Question

For Exercises 11 and 12, use the table below that shows the number of kids registered for baseball and softball

The Westfall Youth Baseball and Softball League charges the following registration fees: ages 7-8, $45$; ages 9-10, $55$; and ages 11-14, $65$.

 Find the total amount of money that League received from baseball and softball registrations.

Step-by-Step Solution

Answer

The money obtained from baseball is $45050$ and from softball is .$29475$

Step 1- Determine the method that will be used

The result of multiplication between the matrices related to the registration fees and count of players will help.

Step 2 – Use the method

Perform the multiplication between the matrices $P=\left[\begin{array}{ccc}350& 320& 180\\ 280& 165& 120\end{array}\right]$

and $R=\left[\begin{array}{c}45\\ 55\\ 65\end{array}\right]$

$\begin{array}{c}PR=\left[\begin{array}{ccc}350& 320& 180\\ 280& 165& 120\end{array}\right]\cdot \left[\begin{array}{c}45\\ 55\\ 65\end{array}\right]\\ =\left[\begin{array}{c}45050\\ 29475\end{array}\right]\end{array}$

Step 3- Make the conclusion

The first row results in 45050 and second results in 29475 which means that the money obtained from Baseball is and from softball is$29475$ because the first row of product matrix represents the baseball and second row represents the softball.