Question

Your mom gives you $5 for a weekly allowance. Your grandpa gives you an amount per chore that you do for him. After doing 7 chores for your grandpa, you have raised a total of $15.50. Write an equation representing the amount of money, y, you have raised after x chores.

Answer 1

The equation
`\[y = 5 + x\]` represents the total amount of money raised
`(\(y\))` as the sum of a fixed weekly allowance
`(\(5\))` from your mom and the earnings
`(\(x\))` from the number of chores done for your grandpa. In mathematical terms, it's a simple linear equation, providing a clear relationship between the total amount and the number of chores completed.

Explanation:

The equation
`\(y = 5 + x\)` encapsulates the financial dynamics of a weekly allowance and earnings from chores. In this mathematical expression,
`\(y\)` signifies the total amount of money raised, (5) represents the fixed weekly allowance provided by your mom, and (x) denotes the variable reflecting the earnings from the chores accomplished for your grandpa. The constant term (5) serves as the baseline financial contribution, independent of the number of chores completed, while the variable term (x) dynamically adjusts the total amount based on the cumulative number of chores.

This equation embodies a linear relationship, where each additional chore contributes a consistent amount
`(\(x\))` to the overall funds. From a mathematical standpoint, this simplicity allows for straightforward interpretation and prediction of the total amount raised as the number of chores
`(\(x\))` increases. It showcases a clear and direct connection between the fixed allowance and the variable earnings, enabling an easy understanding of the financial outcome associated with the completion of each chore.

Linear equations are foundational in mathematics, offering a concise representation of relationships between variables. In this specific scenario, (y = 5 + x) provides a mathematical tool to track and project the total financial outcome as a function of completed chores. It serves as a practical model for financial planning and understanding the interplay between fixed and variable components in the context of a weekly allowance and chore-based earnings.