Question

reagan needs to rent a pickup truck for one day, so she is comparing different rental companies rates.
one rental company charges $55 per day to rent a pickup, with no additional charge per mile driven.
another companys charge of $34 per day includes up to 150 miles. beyond that, the renter is charged $0.25 per mile.
if reagan drives a certain distance, d, the total charges from the two rental companies will be the same amount. which equation can reagan use to find d?
55d = 34 + 0.25(150 - d)
55 = 0.25(150 - d)+34
55 = 34 + 0.25(d - 150)
55d = 0.25(d - 150)+34
now, use the equation you picked to find d.
d = miles

Explanation:

Step1: Analyze the first - company's cost

The first company charges a flat - rate of $55 per day with no additional charge per mile. So the cost $C_1$ for one day is $C_1 = 55$.

Step2: Analyze the second - company's cost

The second company charges $34 per day for up to 150 miles. If Reagan drives $d$ miles and $d>150$, the additional miles are $d - 150$. The cost $C_2$ for the second company is $C_2=34 + 0.25(d - 150)$.

Step3: Set the two costs equal

We want to find when $C_1 = C_2$. So the equation is $55=34 + 0.25(d - 150)$.

Step4: Solve the equation for $d$

First, expand the right - hand side:
$55=34+0.25d-37.5$.
Combine like terms:
$55 = 0.25d - 3.5$.
Add 3.5 to both sides:
$55 + 3.5=0.25d$, so $58.5 = 0.25d$.
Divide both sides by 0.25:
$d=\frac{58.5}{0.25}=234$.

Answer:

The correct equation is $55 = 34+0.25(d - 150)$.
$d = 234$ miles