Question

1. ride-share services

zoom go!: $1.50 per mile + $4 base fee
ride wave: $2 per mile + $3 base fee
analyze the data

1. at what distance do both ride-share services cost the same?

to find the distance both ride-share services cost the same, set the equations equal to each other
__x + = x + __
solve for x

1. which service is the better deal for a 5-mile trip? substitute x=5 into both equations

____

1. which service is the better deal for an 10-mile trip? substitute x=10 into both equations

____
zoom go!
y = __x + __
ride wave
y = __x + __

Explanation:

Step1: Define Cost Equations

Let \( x \) be miles, \( y \) be total cost.
Zoom Go!: \( y = 1.5x + 4 \)
Ride Wave: \( y = 2x + 3 \)

Step2: Find Equal Cost Distance

Set \( 1.5x + 4 = 2x + 3 \).
Subtract \( 1.5x \): \( 4 = 0.5x + 3 \).
Subtract 3: \( 1 = 0.5x \).
Multiply by 2: \( x = 2 \).

Step3: Cost for 5-Mile Trip

• Zoom Go!: \( y = 1.5(5) + 4 = 7.5 + 4 = 11.5 \)
• Ride Wave: \( y = 2(5) + 3 = 10 + 3 = 13 \)

Better: Zoom Go!

Step4: Cost for 10-Mile Trip

• Zoom Go!: \( y = 1.5(10) + 4 = 15 + 4 = 19 \)
• Ride Wave: \( y = 2(10) + 3 = 20 + 3 = 23 \)

Better: Zoom Go!

Answer:

s:

1. Distance: \( \boldsymbol{2} \) miles.
2. 5-mile: Zoom Go!
3. 10-mile: Zoom Go!