Each month, Kaisorn deposits $50.00 onto her public transportation card. It costs her $2.50 per trip to ride the subway. Thom deposits $40.00 on his public transportation card. It costs him $2.00 per trip to ride the subway. If [tex]$x$[/tex] represents the number of trips and [tex]$y$[/tex] represents the amount remaining in each account, which system of equations represents their transportation costs?
[tex]
\begin{array}{l}
50-2.5 x=y \\
40-2 x=y
\end{array}
[/tex]
[tex]$50+2.5 x=y$
$40+2 x=y$
[/tex]
[tex]$50-2.5 y=x$
$40-2 y=x$
[/tex]
[tex]$50+2.5 y=x$
$40+2 y=x$
[/tex]
Answer (2)
Kaisorn's remaining balance y after x trips is modeled by y = 50 − 2.5 x .
Thom's remaining balance y after x trips is modeled by y = 40 − 2 x .
The system of equations representing their transportation costs is formed.
The final system of equations is: 50 − 2.5 x = y 40 − 2 x = y
Explanation
Analyze the problem Let's analyze the given information to form the equations. Kaisorn starts with $50 and spends 2.50 p er t r i p . I f x i s t h e n u mb ero f t r i p s , t h e n t h e am o u n t re mainin g , y , i s g i v e nb y y = 50 - 2.5x$. Thom starts with $40 and spends 2.00 p er t r i p . S o , t h e am o u n t re mainin g , y , i s g i v e nb y y = 40 - 2x$.
Form the equations The system of equations representing their transportation costs is:
Kaisorn: y = 50 − 2.5 x Thom: y = 40 − 2 x
State the final system of equations Therefore, the correct system of equations is:
50 − 2.5 x = y 40 − 2 x = y
Examples
Imagine you're managing a budget for a school trip. You start with a certain amount of money, and each activity costs a specific amount per student. This problem helps you determine how much money is left after a certain number of activities, similar to how Kaisorn and Thom manage their transportation cards. Understanding these equations allows you to plan and track expenses effectively, ensuring you don't run out of funds before the trip ends. This is a practical application of linear equations in everyday financial planning.
The correct system of equations representing Kaisorn and Thom's transportation costs is: 50 − 2.5 x = y and 40 − 2 x = y . This means after spending on trips, their remaining balances decrease based on the number of trips taken.
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