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: The You Move It Company (YMI) advertises that the cost to rent a ​moving truck for one day is $40 plus $1.99 for each mile the truck is ​driven. ​ ​The Drive and Move Company (DM) advertises that the cost to ​rent a moving truck for one day is $60 plus $1.79 for each mile the ​truck is driven. ​ ​Alex wants to rent a single truck to use on both ​Saturday and Sunday on a weekend. ​Part A For what driving distance does it not matter from which company Alex rents the truck? ​ ​ miles. ​ ​If Alex only plans of driving 150 miles over the weekend, which company should he use? ​ ​ ​ ​ ​Part B Give a mathematical explanation as to how you arrived at your answer.​

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Part A: For 100 miles, the cost will be same for both companies.

Part B: Alex should use Drive and Move company as it will cost him less money.

Step-by-step explanation:

Given,

Starting amount of YMI= $40

Per mile charges = $1.99

Let,

x be the number of miles.

y be the total charges.

y = 1.99x+40    Eqn 1

Starting amount of DM = $60

Per mile charges = $1.79

y=1.79x+60    Eqn 2

Part A:

For same charges;

Eqn 1 = Eqn 2

[tex]1.99x+40=1.79x+60\\1.99x-1.79x=60-40\\0.20x=20[/tex]

Dividing both sides by 0.20

[tex]\frac{0.20x}{0.20}=\frac{20}{0.20}\\x=100[/tex]

For 100 miles, the cost will be same for both companies.

Part B:

Total miles = x = 150

Putting x=150 in Eqn 1

y=1.99(150)+40

y=298.5+40

y=$338.50

Putting x=150 in Eqn 2

y=1.79(150)+60

y=268.5+60

y=$328.50

Alex should use Drive and Move company as it will cost him less money.

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