You are renting a limousine that charges certain rates to visit each of the following cities. You need to visit each city once and you need to start in Athens and end in Athens. Use the "Brute Force" Algorithm to find the cheapest route to visit each city and return home again to Athens.

A. B. C. D.

the answer is Athens-Buford-Cu-Dacul-Athens

Step-by-step explanation:

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Way 3 and 4

Step-by-step explanation:

The Algorithm of Brute Force

Let A is Athens,  

Let B is Buford,  

Let C is Cuming,

Let D is Dacula  

Use the "Brute Force" Algorithm to find the cheapest route to visit each city and return home again to Athens, we can see that there are 6 ways to visit each city and return home again to Athens.

Way 1: A→C→D→B→A = 50 + 30 + 70 + 70 = $220

Way 2: A→D→B→C→A = 60 + 70 + 25 + 50 = $205

Way 3: A→D→C→B→A = 60 + 30 + 25 + 70 = $185

Way 4: A→B→C→D→A = 70 + 25 + 30 + 60 = $185

Way 5: A→B→D→C→A = 70 + 70 + 30 + 50 = $220

Way 6: A→C→B→D→A = 50 + 25 + 70 + 60 = $205

Way 3 and 4 are the cheapest so we choose them.

starting with:    

5 + x - 12 = 2x - 7   

5 + x - 12 - x = 2x - 7 - x (subtract x from both sides)   

5 - 12 = x - 7 (combine and cancel x's from both sides)   

5 - 12 + 7 = x - 7 + 7 (add 7 to both sides)   

0 = x (add numbers together on both sides)       

so in order for the equation to be true, x must be 0.   

trying x = -0.5   

5 + x - 12 = 2x - 7 (original equation)   

5 + -0.5 - 12 = 2(-0.5) - 7 (plug in value of x)   

5 + -0.5 - 12 = -1 - 7 (did multiplication)   

-7.5 = -8 (did addition on both sides)       

since -7.5 is obviously not equal to -8, the value of -0.5 for x is wrong.   

trying x = 0   

5 + x - 12 = 2x - 7 (original equation)   

5 + 0 - 12 = 2(0) - 7 (plug in value of x)   

5 + 0 - 12 = 0 - 7 (did multiplication)   

-7 = -7 (did addition on both sides)       

since -7 equals -7, that demonstrates that the value of 0 for x is correct.   

trying x = 1   

5 + x - 12 = 2x - 7 (original equation)   

5 + 1 - 12 = 2(1) - 7 (plug in value of x)   

5 + 1 - 12 = 2 - 7 (did multiplication)   

-6 = -5 (did addition on both sides)       

since -6 is obviously not equal to -5, the value of 1 for x is wrong.

explanation:

step-by-step explanation: