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}{c}
50-2.5 x=y \\
40-2 x=y
\end{array}
[/tex]
[tex]
\begin{array}{c}
50+2.5 x=y \\
40+2 x=y
\end{array}
[/tex]
[tex]
\begin{array}{c}
50-2.5 y=x \\
40-2 y=x
\end{array}
[/tex]
[tex]
\begin{array}{c}
50+2.5 y=x \\
40+2 y=x
\end{array}
[/tex]
Answer (2)
Kaisorn's remaining balance is modeled as y = 50 − 2.5 x .
Thom's remaining balance is modeled as 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
Problem Analysis Let's analyze the problem. Kaisorn starts with $50 and spends $2.50 per trip. Thom starts with $40 and spends $2.00 per trip. We want to find a system of equations that represents the amount of money remaining on their cards after a certain number of trips.
Kaisorn's Equation For Kaisorn, the amount remaining, y , is the initial amount, $50, minus the cost per trip, 2.50 , t im es t h e n u mb ero f t r i p s , x . T hi s g i v es u s t h ee q u a t i o n : y = 50 − 2.5 x $
Thom's Equation For Thom, the amount remaining, y , is the initial amount, $40, minus the cost per trip, 2.00 , t im es t h e n u mb ero f t r i p s , x . T hi s g i v es u s t h ee q u a t i o n : y = 40 − 2 x $
System of Equations Combining these two equations, we get the system of equations: { y = 50 − 2.5 x y = 40 − 2 x
Final Answer Therefore, the correct system of equations is: { 50 − 2.5 x = y 40 − 2 x = y
Examples
Understanding transportation costs can help you budget your monthly expenses. For example, if you know the cost per trip and your monthly deposit, you can calculate how many trips you can take each month. This can also help you compare different transportation options and choose the most cost-effective one. By modeling your expenses with equations, you can make informed decisions about your spending and save money.
The system of equations representing Kaisorn's and Thom's transportation costs is: { 50 − 2.5 x = y 40 − 2 x = y . This shows the remaining balance after spending on subway trips based on their deposits and trip costs.
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