two multipedes were dancing together at a party and trying hard not to trip over each others feet.One smiled at the other and said if you could give me 2 of your legs we'd have the same number the other replied if i had two of yours id have three times as many.legs as you .How many legs did each have ?

number of legs of one (the smiler) ---- x

number of legs of the other ---- y

smiling one said:
x+2 = y-2 -----> x - y = -4 **

other said:
y+2 = 3(x-2)
y+2 = 3x - 6
3x - y = 8 ***

subtract: *** - **
2x = 12
x = 6 , then y = 10

state your conclusion

Let's solve this step by step.

Let's assume one multipede has 'x' number of legs, and the other multipede has 'y' number of legs.

According to the conversation, the first multipede says, "If you could give me 2 of your legs, we'd have the same number." This can be expressed as an equation: x + 2 = y.

The second multipede says, "If I had two of yours, I'd have three times as many legs as you." This can be expressed as an equation: y + 2 = 3(x).

Now, we can solve these equations simultaneously to find the values of x and y.

Step 1: Substitute the value of x + 2 from the first equation into the second equation:
(y + 2) = 3(x)
Substituting x + 2 as y in the second equation, it becomes:
(x + 2 + 2) = 3(x)
Simplifying, we have:
x + 4 = 3x

Step 2: Subtract x from both sides of the equation to isolate the variables:
4 = 2x

Step 3: Divide both sides by 2 to solve for x:
2 = x

Now that we have found x, we can substitute it back into the first equation to find y:
x + 2 = y
2 + 2 = y
4 = y

So, one multipede has 2 legs, and the other has 4 legs.

To solve this problem, let's break it down step by step:

Let's assume the number of legs of the first multipede is "x," and the number of legs of the second multipede is "y."

According to the first statement, if the first multipede received two legs from the second multipede, they would have the same number of legs. This can be written as:
x + 2 = y

According to the second statement, if the second multipede received two legs from the first multipede, they would have three times as many legs as the first multipede. This can be written as:
y + 2 = 3(x)

Now we have a system of two equations with two unknowns:
x + 2 = y
y + 2 = 3x

To solve this system, we can use substitution or elimination. Let's use substitution:

Rearrange the first equation to solve for y in terms of x:
y = x + 2

Substitute this value of y into the second equation:
x + 2 + 2 = 3x
x + 4 = 3x

Now, subtract x from both sides to isolate the x term:
4 = 2x

Finally, divide both sides by 2 to solve for x:
x = 2

Now, substitute the value of x back into the first equation to find y:
y = x + 2
y = 2 + 2
y = 4

Therefore, the first multipede has 2 legs, and the second multipede has 4 legs.

So, the first multipede has 2 legs, and the second multipede has 4 legs.