Question

the price of a climbing trip to mount kilimanjaro includes an initial fee plus a constant fee per meter.
the table compares the total distance of a trip (in meters) and the price of the trip (in dollars).
distance (meters) price (dollars)
80 115.40
110 119.30
140 123.20
how far can you climb for $131?
_____ meters
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Explanation:

Step1: Find per-meter fee

First, calculate the change in distance and price between two points. Using the first two rows:
Change in distance: $110 - 80 = 30$ meters
Change in price: $119.30 - 115.40 = 3.90$ dollars
Per-meter fee: $\frac{3.90}{30} = 0.13$ dollars per meter

Step2: Find initial fee

Use the first data point ($d=80$, $P=115.40$) and the linear model $P = md + b$, where $m=0.13$, $d$ is distance, $b$ is initial fee.
$115.40 = 0.13 \times 80 + b$
$115.40 = 10.4 + b$
$b = 115.40 - 10.4 = 105$ dollars

Step3: Solve for distance at $131$

Set $P=131$ in the linear equation $P = 0.13d + 105$:
$131 = 0.13d + 105$
$0.13d = 131 - 105$
$0.13d = 26$
$d = \frac{26}{0.13} = 200$

Answer:

200 meters