Question

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

A 50 − 2.5x = y
  40 − 2x = y
B 50 + 2.5x = y
  40 + 2x = y
C 50 − 2.5y = x
  40 − 2y = x
D50 + 2.5y = x
  40 + 2y = x

Answer 1

The answer is
"A"
50 - 2.5x = y
40 - 2x = y

Answer 2

A. 50 − 2.5x = y

40 − 2x = y

Explanation:

We know that x represents the number of trips and y represents the amount remaining in each account, then, let's think in an example; after the first trip x = 1, therefore, Kaisorn's account must decrease from $50 to $50 - $2.5 = $47.5 = y, and Thom's account must decrease from $40 to $40 - $2 = $38 = y. Replacing x = 1 in each case gives:

A

50 − 2.5(1) = y

47.5 = y

40 − 2(1) = y

38 = y

B

50 + 2.5(1) = y

52.5 = y

40 + 2(1) = y

42 = y

C

50 − 2.5y = (1)

y = (1 - 50)/(-2.5)

y = 19.6

40 − 2y = (1)

y = (1 - 40)/(-2)

y = 19.5

D

50 + 2.5y = (1)

y = (1 -50)/2.5

y = -19.6

40 + 2y = (1)

y = (1 - 40)/(2)

y = -19.5

As it can be seen, option A is the correct one.