greg needs to hire someone to clear his driveway of snow this winter season. Look in description

Question

a neighbor has a plow attached to his truck and charges $30 for each time he plow the driveway. mel's landscaping runs a snow clearing business and charges $50 for the first time they plow and $25 for each additional time they plow. write and solve an equation to determine when the costs of each option are the same. under what conditions would greg choose his neighbor? mel's landscaping?

Answer 1

Neighbor: $30 * each driveway

Mel's Landscaping: $50 + $25*each driveway after the first one

Variables:

C= cost

X = each driveway

C_n = total cost of neighbor

C_m = total cost of Mel's Landscaping

Equations:

C_n = 30*X

C_m= 50 + 25 (X - 1) --> we need to subtract one because the 1st time is $50 and the second time is $25

to solve for when both options are the same we need to set the equations equal to each other

30X = 50 + 25(x-1)

30X= 50 + 25X - 25

30X- 25X = 50-25

5X = 25

X = 5, when greg needs his driveway plowed 5 times, both options are equal

for the 6th time:

C_n= 30* 6 = 180

and C_m= 50 + 25 (6 - 1) = 175

Mel's Landscaping would be better for 6 or more times

for the 4th time:

C_n= 30* 4 = 120

and C_m= 50 + 25 (4 - 1) = 125

Greg's neighbor would be better for 4 or less times