Question

Yak Travel Agency arranges trips for climbing Mount Everest. For each trip, they charge an initial fee in addition to \$0.15$0.15dollar sign, 0, point, 15 for each vertical meter climbed. For instance, the price for climbing all the way to the summit, which is 350035003500 meters above the base of the mountain, is \$645$645dollar sign, 645.

Let yyy represent the fee (in dollars) of a trip where they climbed xxx vertical meters.

Complete the equation for the relationship between the fee and vertical distance.

Answer 1

`y = 120 + 0.15x`

Explanation:

Given

`Additional\ Fee = \$0.15` per vertical meter

`y = fee` per x meter

`x = vertical\ meter`

For:

`x = 3500` ---
`y = 645`

Required

Determine the equation that relates y to x

Let the initial fee be represented with m

The equation that relates y to x is:

`y = Initial\ Fee + Additional\ Fee * Vertical\ Meter`

This gives

`y = m + 0.15 * x`

We need to first solve for m

From the question,

`x = 3500` when
`y = 645`

So:

`645 = m + 0.15 * 3500`

`645 = m + 525`

Make m the subject

`m = 645 - 525`

`m = 120`

So, the initial fee is $120

Substitute 120 for m in
`y = m + 0.15 * x`

`y = 120 + 0.15 * x`

`y = 120 + 0.15x`

Hence, the required equation is:
`y = 120 + 0.15x`