1) A truck driver is paid on a per-mile basis. He wants to develop a formula to

Question

1) A truck driver is paid on a per-mile basis. He wants to develop a formula to forecast how much money he will earn (or loose) in each trip. He estimates that diesel fuel costs $3.45 a gallon and the consumption is 12 gallons per 100 miles. Other maintenance costs are estimated at 16 cents per mile, and 5 cents per mile for overhead cost. He has found that fixed expenses are estimated at $115 on each trip.
(a) How much will he have to drive to breakeven?
(b) How much will he earn in a 1255-mile trip?
(c) If he makes three different trips for 450, 600, and 1600 miles each in one week, how much are his earnings?

Explanation / Answer

Start with the preliminary work

Get everything to cost per mile except for the fixed expense estimate

let x=the number of miles

12 gallons per 100 miles = .12 gallons per mile

.12 gallons per mile at $3.45= .12*3.45=$.414 per mile

Maintenence = 16 cents per mile

Overhead = 5 cents per mile

Since there was never a value given for the amount of money he made per mile, I will use the $ symbol and you can replace this with the actual value. I will write an expanded equation then simplify

Expanded

f(x)=$x-.414x-.16x-.05x-115

      =$x-(.414x+.16x+.05x)-115

Simplified

f(x)=$x-.624x-115

a) $x-.624x-115=0

   Solve for x

     x($-.624)=115

     x=115/($-.624)

b)for this substitute 1255 in for x in the simplified equation and it will spit out the answer

c) substitute each value into the equation separately then add the results together

Related Questions

Navigate

• Browse (All)
• Browse 1
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.