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) 707070 114.1114.1114, point, 1 100100100 118118118 130130130 121.90121.90121, point, 90 How far can you climb for \$131$131dollar sign, 131?
Answers
Given:
The price of a climbing trip to Mount Kilimanjaro includes an initial fee plus a constant fee per meter.
Table:
Distance (meters) Price (dollars)
70 114.1
100 118
130 121.90
To find:
Meters that can be climbed for $ 131
Solution:
Finding the price of climbing the trip of 1 m:
From the given table we can see that
The common difference in the distance in meters or the increase in distance is 30 m ..... [100 - 70 = 30 m & 130 - 100 = 30 m]
Also, the increase in the price in dollars is → 118 - 114.1 = $ 3.9 & 121.90 - 100 = $ 3.9
So, we get, the price of climbing a trip of 30 m = $3.9
∴ The price of climbing a trip of 1 m = = $ 0.13 ← initial fee for climbing every meter
Finding the initial fee & the constant fee per meter:
(i) Taking the distance = 70 m and total price = $ 114.1
∴ The initial price of climbing 70 m = $0.13 * 70 = $ 9.1
∴ The constant fee per meter = $ 114.1 - $ 9.1 = $ 105
(ii) Taking the distance = 100 m and total price = $ 118
∴ The initial price of climbing 100 m = $0.13 * 100 = $ 13
∴ The constant fee per meter = $ 118 - $ 13 = $ 105
(iii) Taking the distance = 130 m and total price = $ 121.90
∴ The initial price of climbing 130 m = $0.13 * 130 = $ 16.9
∴ The constant fee per meter = $ 121.90 - $ 16.9 = $ 105
From the above calculation we can form a linear equation as:
where
x = total price of a climbing trip
y = distance covered in a climbing trip
Finding the distance covered with a price of the climbing trip of $ 131:
here we have x = $131 and by substituting the value of x in the linear equation we will find the value of y
131 = 0.13x +105
⇒ 0.13x = 131 - 105
⇒ 0.13x = 26
⇒ x =
⇒ x = 200 m
Thus, we can climb a trip of 200 m to Mount Kilimanjaro for $131.
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