Question

Steven is moving to another city next weekend and wants to rent a moving truck. The rental rates for two companies in his area are shown below. Each company charges an initial fee for renting the truck, plus an additional amount per mile.

Answer 1

Company (1) charges $1.12 per mile and company (2) charges $0.85 per mile

Company (2) is $7.4 cheaper.

Explanation:

From the tables given in the picture,

Let the equation representing the rental 'y' and distance traveled 'x' is represented by,

y = mx + b

For company (1),

Here m = per mile rental charges = Slope of the graph

b = Initial charges

Since slope of the line passing through two points
`(x_1,y_1)` and
`(x_2,y_2)` is given by,

m =
`(y_2-y_1)/(x_2-x_1)`

Therefore, slope of the line passing through (30, 53.55) and (60, 87.15) will be,

m =
`(87.15-53.55)/(60-30)` = $1.12 per mile

So the equation will be,

y = 1.12x + b

Since this line passes through (30, 53.55),

53.55 = 1.12(30) + b

b = 53.55 - 33.6

b = 19.95

So the expression representing charges for the company (1) will be,

y = 1.12x + 19.95

For company (2),

Per mile charges = slope of the line

m =
`(78-56.75)/(50-25)`

m = $0.85 per mile

Equation for the charges will be,

y = 0.85x + b

Since this line passes through (25, 56.75),

56.75 = 0.85(25) + b

b = 56.75 - 21.25

b = 35.5

Therefore, equation representing total charges for company (2) will be,

y = 0.85x + 35.5

By comparing per mile charges,

Company (1) charges $1.12 per mile and company (2) charges $0.85 per mile

Steven plans to drive 85 km in rental truck.

Charges for company (1),

y = 1.12x + 19.95

y = 1.12(85) + 19.95

y = $115.15

Charges for company (2),

y = 0.85x + 35.5

y = 0.85(85) + 35.5

y = $107.75

Difference in charges of both the companies = 115.15 - 107.75 = $7.4

Therefore, company (2) is $7.4 cheaper.