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Each month, Kaisorn deposits [tex]$\$[/tex]50.00[tex]$ onto her public transportation card. It costs her $[/tex]\[tex]$2.50$[/tex] per trip to ride the subway.
Thom deposits [tex]$\$[/tex]40.00[tex]$ on his public transportation card. It costs him $[/tex]\[tex]$2.00$[/tex] 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]\[
\begin{array}{c}
50 - 2.5x = y \\
40 - 2x = y
\end{array}
\][/tex]

A.
[tex]\[
\begin{array}{c}
50 - 2.5x = y \\
40 - 2x = y
\end{array}
\][/tex]

B.
[tex]\[
\begin{array}{c}
50 + 2.5x = y \\
40 + 2x = y
\end{array}
\][/tex]

C.
[tex]\[
\begin{array}{c}
50 - 2.5y = x \\
40 - 2y = x
\end{array}
\][/tex]

D.
[tex]\[
\begin{array}{c}
50 + 2.5y = x \\
40 + 2y = x
\end{array}
\][/tex]



Answer :

GinnyAnswer
To determine which system of equations represents Kaisorn and Thom's transportation costs, we need to understand how their deposits and trip costs interact.

1. Kaisorn's Calculation:
- Initial Deposit: Kaisorn deposits \[tex]$50.00 each month. - Cost per Trip: \$[/tex]2.50 per trip.

Let's denote:
- [tex]\( x \)[/tex] as the number of trips Kaisorn takes.
- [tex]\( y \)[/tex] as the amount remaining on her card.

Since each trip reduces her balance by \[tex]$2.50, the remaining amount after \( x \) trips can be represented by: \[ y = 50 - 2.5x \] 2. Thom's Calculation: - Initial Deposit: Thom deposits \$[/tex]40.00 each month.
- Cost per Trip: \[tex]$2.00 per trip. Similarly, let's denote: - \( x \) as the number of trips Thom takes. - \( y \) as the amount remaining on his card. Since each trip reduces his balance by \$[/tex]2.00, the remaining amount after [tex]\( x \)[/tex] trips can be represented by:
[tex]\[ y = 40 - 2x \][/tex]

Based on the above calculations, the system of equations representing Kaisorn and Thom's transportation costs is:
[tex]\[ \begin{array}{c} 50 - 2.5x = y \\ 40 - 2x = y \end{array} \][/tex]

The correct choice is:
[tex]\[ \begin{array}{c} 50 - 2.5x = y \\ 40 - 2x = y \end{array} \][/tex]

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