Answer:
y = -1.2x + 30
x = 22
x = 15
Step-by-step explanation:
<u>Part A</u>
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.
<u>Part B</u>
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.
