Question

each month, kaison 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 ( x ) represents the number of trips and ( y ) represents the amount remaining in each account, which system of equations represents their transportation costs? \\( \

$$\begin{array}{|c|c|c|} \\hline 50 - 2.5y = x \\\\ 40 - 2y = x & 50 + 2.5x = y \\\\ 40 + 2x = y & 50 - 2.5x = y \\\\ 40 - 2x = y \\\\ \\hline 50 + 2.5y = x \\\\ 40 + 2y = x & \\\\ \\hline \\end{array}$$

\\)

Explanation:

Step1: Analyze Kaisorn's equation

Kaisorn deposits $50, and each trip costs $2.50. The remaining amount \( y \) is the initial deposit minus the total cost of trips. The total cost of \( x \) trips is \( 2.5x \), so her equation is \( y = 50 - 2.5x \).

Step2: Analyze Thom's equation

Thom deposits $40, and each trip costs $2.00. The remaining amount \( y \) is the initial deposit minus the total cost of trips. The total cost of \( x \) trips is \( 2x \), so his equation is \( y = 40 - 2x \).

Answer:

\(

$$\begin{cases} 50 - 2.5x = y \\ 40 - 2x = y \end{cases}$$

\) (the third system of equations)