Question

select the correct answer.
jamal is comparing his transportation options for an upcoming trip. hes considering a rental car and a taxi service. based on his planned routes during his trip, he expects a taxi service would cost about $128. jamal could also get a rental car for a daily rate and unlimited miles. if jamal’s trip will last 4 days and he expects to pay about $24 for gas, which graph shows the range of car rental rates that would be cheaper than the taxi service?
a.
<---(19)---(21)---(23)---(25)---⚪(27)---(29)---(31)---(33)---(35)---(37)---(39)--->

b.
<---(19)---(21)---(23)---(25)---●(27)---(29)---(31)---(33)---(35)---(37)---(39)--->

c.
<---(19)---(21)---(23)---(25)---⚪(27)---(29)---(31)---(33)---(35)---(37)---(39)--->
--->

d.
<---(19)---(21)---(23)---(25)---(27)---(29)---(31)---⚪(33)---(35)---(37)---(39)--->

Explanation:

Step1: Define variables

Let \( d \) be the daily rental rate of the car.

Step2: Set up the inequality

The total cost of the rental car for 4 days plus gas should be less than the taxi cost. So, \( 4d + 24 < 128 \).

Step3: Solve the inequality

Subtract 24 from both sides: \( 4d < 128 - 24 \)
\( 4d < 104 \)
Divide both sides by 4: \( d < \frac{104}{4} \)
\( d < 26 \)

Step4: Analyze the graph

We need a graph with an open circle at 26 (since \( d < 26 \), not \( d \leq 26 \)) and the arrow pointing to the left (for values less than 26). Option A has an open circle at 26 and the arrow left.

Answer:

A