Lunch Accounts
Enrique has $50 in his lunch account and spends $5 per day from the account. Maya has $46 in her lunch account and spends $4 per day from the account. Which equations model the situation?
A. $50-5x=y$ and $46-4x=y$
B. $5x+50=y$ and $4x+46=y$
C. $5x-50=y$ and $4x-46=y$
D. $5-50x=y$ and $4-46x=y
Answer (2)
The equations that model the lunch account situation for Enrique and Maya are 50 − 5 x = y and 46 − 4 x = y . This choice corresponds to option A. Both equations represent the initial amount minus the amount spent per day over a number of days.
;
Define variables: Let x be the number of days and y be the amount of money left.
Enrique's equation: The amount left is the initial amount minus the spending: y = 50 − 5 x .
Maya's equation: Similarly, for Maya: y = 46 − 4 x .
The equations that model the situation are: 50 − 5 x = y and 46 − 4 x = y .
Explanation
Problem Analysis Let's analyze the problem. Enrique starts with $50 and spends $5 each day. Maya starts with $46 and spends $4 each day. We want to find the equations that represent the amount of money each person has in their account after a certain number of days.
Equation Formulation Let x represent the number of days and y represent the amount of money left in the account. For Enrique, the equation is the initial amount minus the amount spent per day times the number of days: y = 50 − 5 x . For Maya, the equation is the initial amount minus the amount spent per day times the number of days: y = 46 − 4 x .
Final Equations Therefore, the equations that model the situation are 50 − 5 x = y and 46 − 4 x = y .
Examples
Understanding how to model financial situations with linear equations is very useful in everyday life. For example, if you are saving money for a specific goal, like buying a new phone, you can use a similar equation to track your progress. If you start with $20 and save $5 each week, the equation y = 20 + 5 x can help you determine how much money you'll have after x weeks. Similarly, if you are paying off a debt, like a credit card, you can use a linear equation to model how much you owe over time. If you owe $500 and pay $25 each month, the equation y = 500 − 25 x can help you track your debt. These equations help you plan and manage your finances effectively.
