Question

Flying lessons cost $645 for an 8-hour course and $1425 for a 20-hour course. Both prices include a fixed insurance fee. a. Write an equation for the cost,C, of flying lessons in terms of the length,h, of the course in hours. Hint: Find two points ( h , C

Answer 1

Y = $125 + $65x

Explanation:

in order to write an euation for the cost and flying lesson, high and low method will be used

cost hours

High $1425 20

Low $645 8

780 12

varaible cost per hr(b) = $780/12 = $65

equation of straight line

Y = a + bx

a = fixed cost , b = variable cost , x = hours of the course , Y = total cost

to calculate a , using high

therefore Y = $1425 , x = 20

1425 = a + 65(20)

1425 - 1300 = a

a = $125

the equation is therefore,

Y = $125 + $65x

Answer 2

Check Explanation

Explanation:

a) Let the fixed insurance fee be A and the rate charged per hour be b

The equation for the cost, C, of flying lessons in terms of length, h, of the course in hours is given by

C = A + bh

b) The two points (h, C) given in the question are (8, 645) and (20, 1425)

c) To find the equation of the line passing through these two points,

equation of a straight line iS given by

y = mx + c (where m = slope of the line and c = intercept)

denoting hours (h) as x and Cost (C) as y

645 = 8m + c

1425 = 20m + c

Solving this simultaneous equation,

m = 65 dollars/hour and c = 125 dollars

The equation of the straight line is

y = 65x + 125

Written in the variables of the question,

C = 65h + 125

This shows that the fixed insurance fee, called A in part (a) = $125

And the rate charged per hour called b in part (a) = $65/hour

Hope this Helps!!!