Question

Devin has $30 on his bus card. Every time he rides a bus, $1.20 is deducted from the value on his card. The amount if money he has on his card, y dollars, is a function of the number of times he rides the bus, x.

Part A
• Find an equation in slope-intercept form to represent the function.
• Find the number of bus rides Devin has taken if he has $3.60 on his card.

Write your answers and your work or explaination in the space below.

Part B
Rebecca has a bus card as well. The amount of money left on her card, y dollars, after taking x rides on the bus can be represented by the function y=-1.4x+33. After how many rides on the bus would both Devin and Rebecca have the same amount of value on their bus card?

Write your answer and your work or explaination in the soace below.

Answer 1

y = -1.2x + 30

x = 22

x = 15

Explanation:

Part A

Initially, Devin has $30. Then every time he rides the bus, $1.20 is taken away: y = 30 - 1.2x

Therefore, in slope-intercept form: y = -1.2x + 30

If he has $3.60 on his card, then y = 3.60, so substitute this into the above equation and solve for x:

3.60 = -1.2x + 30

subtract 30 from both sides: -26.4 = -1.2x

divide both sides by -1.2: 22 = x

Therefore Devin has ridden the bus 22 times if he has $3.60 on his card.

Part B

Rebecca: y = -1.4x + 33

To determine how many rides on the bus Devin and Rebecca would need to take to have the same amount of value of their bus card, simply equate the equations and solve for x:

Rebecca = Devin

y = y

-1.4x + 33 = 30 - 1.2x

subtract 33 from both sides: -1.4x = -3 - 1.2x

Add 1.2x to both sides: -0.2x = -3

Divide both sides by -0.2: x = 15

Therefore, Devin and Rebecca would both have to take 15 rides on the bus to have the same amount of value of their bus card.