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trasher [3.6K]
3 years ago
13

Each inhabitant of a remote village always tells the truth or always lies. A villager willgive only a ""Yes"" or ""No"" response

to a question a tourists asks. Suppose you are a tourist visiting this areaand come to a fork in the road. One branch leads to the ruins you want to visit; the other branch leads deepinto the jungle. A villager is standing at the fork in the road. What one question can you ask the villager todetermine which branch to take? Justify your answer.
Mathematics
1 answer:
pshichka [43]3 years ago
4 0

Step-by-step explanation:

This is actually a very old riddle, but it is two guards and two doors life death .

So let's apply the same logic to this one.

You only meet one villager and you don't know if he is one of the ones who only tells the truth or always lies, to answer this riddle, the question is actually to an hypothetical third party, another villager, not present, this is a little convoluted so bear with me:

(Pointing to one of the roads): If I asked another villager if this road would lead me to the ruins, would he be correct?

If the villager is a truth one, the true-villager, would tell you that the liar-villager would say no (thus leading you to the jungle).

  • Let's analyze this one, so the villager always tells the truth, and you happen to be pointing to the right direction (ruins), he is answering, that if you would ask another villager whether that is the correct road, that villager would say yes, since you are pointing at the right direction, a liar would tell you no, because the liar would point you to the other road as the correct (jungle), so the true-villager will say no
  • If you happen to be pointing to the wrong direction (jungle), he is answering, that if you would ask another villager whether that is the correct road, that villager would say yes, since you are pointing at the wrong direction, the truth-villager would tell you no, because the liar would point you to the wrong road as the correct (jungle), so the villager will say no

Therefore, no matter what villager you run into, the question will always lead you to the jungle, and therefore you pick the other road.

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Solve for w: -4(w+1)=-24 Please explain this like you would a 2 year old and please explain it so it is the easiest way to solve
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Answer:

Step-by-step explanation:

The first step in solving an equation is to look at it. Identify where the variable is that you're interested in, and see what operations are being performed on that variable.

Here, the variable w has 1 added to it, and the sum is multiplied by -4. The variable is only on the left side of the equation, and is inside parentheses. Inside parentheses, the coefficient of the variable is 1.

These observations tell you that, in some order, you will need to undo the operations of multiplication and addition, and you will have to eliminate parentheses.

You also observe that the multiplication factor of the parentheses (-4) is a factor of the constant on the right side of the equation (-24). This means you have a couple of options for solving this equation:

  1. eliminate parentheses first, using the distributive property
  2. divide by -4 first, to undo the multiplication

The second method is actually faster. We'll illustrate that one first.

__

Divide both sides of the equation by -4 to undo the multiplication by -4.

  -4(w +1)/(-4) = -24/(-4) . . . . . we have indicated the division we want to do

  w +1 = 6 . . . . . . . . . . . . . . . . here is the result of that division

Now, we can add the opposite of +1 to eliminate the constant from the left side. As with all operations on equations, we must do the same thing to both sides. This means we add -1 to both sides of the equation:

  w +1 -1 = 6 -1 . . . . . . we have indicated the addition we want to do

  w = 5 . . . . . . . . . . .  here is the result of that addition

The solution of the equation is ...

  w = 5

__

Often, when parentheses are involved, the numbers are such that the solution method is not as simple as what we just did. In those cases, you would take the approach of eliminating parentheses first. For this equation, it looks like this:

  -4(w +1) = -24 . . . . . . . given

  -4w -4 = -24 . . . . . . . . use the distributive property to eliminate parentheses

We want the variable term by itself, so we need to eliminate the constant -4 that is added on the left. To do that, we add its opposite. This means we add +4 to both sides of the equation.

  -4w -4 +4 = -24 +4 . . . . . . indicating the addition of +4

  -4w = -20 . . . . . . . . . . . . . the result of adding +4

Here, w is multiplied by -4. We want w by itself, so we want to undo that multiplication. That means we want to divide both sides of the equation by -4.

  -4w/(-4) = -20/(-4) . . . . . . indicate the division

  w = 5 . . . . . . . . . . . . . . . . the result of doing the division

The solution of the equation is ...

  w = 5

_____

Our basic approach is to <em>undo the operations done to the variable, in the reverse of the order in which they are done</em>. In that process, we observe the rules of equality: <em>whatever operation you do to one side of the equation must also be done to the other side</em>. (My teacher called this last rule: "keep the equal sign sacred.")

You can always use the distributive property for factoring, collecting terms, or eliminating parentheses.

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