Problem 11 - Algebra 2

Question

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 \(11-14, \$ 65\) $$ \begin{array}{|c|c|c|} \hline \text { Age } & \text { Baseball } & \text { Softball } \\ \hline 7-8 & 350 & 280 \\ \hline 9-10 & 320 & 165 \\ \hline 11-14 & 180 & 120 \\ \hline \end{array} $$ Find the total amount of money the league received from baseball and softball registrations.

Step-by-Step Solution

Answer

The league received $74,525 from registrations.

Step 1: Calculate Total Fees for Baseball

To find the total fees collected for baseball, we need to multiply the number of players in each age group by their respective registration fees. - Ages 7-8: 350 players * $45 = $15,750 - Ages 9-10: 320 players * $55 = $17,600 - Ages 11-14: 180 players * $65 = $11,700 The total fees collected for baseball are $15,750 + $17,600 + $11,700 = $45,050.

Step 2: Calculate Total Fees for Softball

Now, we calculate the total fees collected for softball by multiplying the number of players in each age group by their respective registration fees. - Ages 7-8: 280 players * $45 = $12,600 - Ages 9-10: 165 players * $55 = $9,075 - Ages 11-14: 120 players * $65 = $7,800 The total fees collected for softball are $12,600 + $9,075 + $7,800 = $29,475.

Step 3: Calculate Total Fees from Both Baseball and Softball

To find the total amount of money the league received, we add the amounts collected from baseball and softball. The total amount is $45,050 (baseball) + $29,475 (softball) = $74,525.

Key Concepts

Arithmetic Calculations

In this exercise, we dealt with the task of calculating registration fees by evaluating numbers through arithmetic calculations. For arithmetic problems like this, multiplication and addition are crucial operations.
To solve for total registration fees:

• First, multiply the number of kids by their registration fee for each category.
• Then, sum up the results of all age groups together for each sport.

In the given exercise:

• For Baseball, ages 7-8 required multiplying 350 players by $45, yielding a result of $15,750.
• Similarly, for each age group and sport, repeat these calculations.

Breaking down the total as above aids in getting the precise total amount of money involved. So remember, the main arithmetic operations here are multiplication to calculate individual age groups and addition to get the totals for baseball and softball.
These methods equip you to find solutions efficiently, ensuring you accurately sum large sets of numbers.

Data Interpretation

Data interpretation involves understanding and processing the information presented, such as tables, charts, or graphs. In this problem, a table shows us the number of players registered for baseball and softball by age group.
Interpreting this data requires us:

• To notice the structure, which organizes information neatly into categories like ages, sports, and numbers of players.
• To connect these numbers with the registration fee rates for each age group.

By interpreting the data, we find relationships and develop a strategy to solve for the total amount.
Therefore, part of data interpretation is not just looking at raw numbers but understanding what they represent and how to process them for a required result.
Always examine such tables carefully, noting specific categories and their implications for solving problems.

Step-by-Step Solutions

A step-by-step solution is like a road map leading you from problem to solution sequentially. This method ensures clarity and prevents oversight.
Here's how to use step-by-step solutions effectively:

• Approach the problem by breaking it into smaller, manageable parts.
• Explicitly solve each part, as done in calculating fees for baseball and softball individually before combining them.

Every step is crucial as it builds upon the previous one, leading to an accurate solution.
In this problem, each calculation step for baseball and softball was shown distinctly before merging them into one total sum.
Such structured steps aid in understanding the logic behind each calculation, ensuring thoroughness and precision. This guides you through the entire journey of solving complex problems methodically.