Question

96 POINTS!!!! PLEASE HELP!

Answer 1

Answer:

21 years

Step-by-step explanation:

M: distance she drives (miles)

G: no. of gallons used

125/6000 = 1/48

G = M/48

Or

M = 48G

M = 12000

12000 = 48G

G = 250 gallons

Each gallon: $2.4

Cost = 2.4 × 250 = $600

Evan's cost:

(12000/30) × 2.4 = $960 per year

Anna's fuel cost per year: $600

23740 + 960t = 31140 + 600t

360t = 7400

t = 20.556

Answer 2

A. I suppose the horizontal axis represents the amount of miles Anna drives. You're asked to use the graph to find an equation for the line. You know two points it passes through; this is enough to determine the slope of the line:

$\dfrac{250-125}{12,000-6,000}=\dfrac{125}{6,000}=\dfrac1{48}$

Now use the point-slope formula to get the line's equation. Using the leftmost point, for instance, we have

$y-125=\dfrac1{48}(x-6,000)\implies y=\dfrac x{48}$

This is to say, the amount of fuel $y$ (in gal) that Anna uses is given exactly by dividing the distance traveled $x$ (in mi) by 48.

B. Driving 12,000 mi requires 250 gal of fuel (according to both the rightmost point on the graph as well as the value of $y$ in the previous equation for $x=12,000$). She pays $2.40 per gal, so the total cost for 250 gal is

($2.40/gal) * (250 gal) = $600

C. Evan's car uses approximately

(12,000 mi) / (30 mi/gal) = 400 gal

per year, which costs him an annual total of about

(400 gal) * ($2.40/gal) = $960

We need to know the price of Anna's car to answer the actual question, though...