Question

In Lewis Carroll’s Through the Looking Glass, Tweedledum says, "The sum of your weight and twice mine is 361 pounds." Tweedledee replies, "The sum of your weight and twice mine is 362 pounds." Find both of their weights.

Answer 1

Answer:

Tweedledum weights 120 pounds and Tweedledee 121 pounds.

Step-by-step explanation:

If we say that $W_1$ is the weight of Tweedledum and $W_2$ is the weight of Tweedledee, according to what they say we can write the equations:

$W_2+2W_1=361\ pounds$

$W_1+2W_2=362\ pounds$

We can solve this easily by substitution for example.

From the first equation we can write:

$W_2=361\ pounds-2W_1$

And substitute in the second equation:

$W_1+2(361\ pounds-2W_1)=362\ pounds$

Which means:

$W_1+722\ pounds-4W_1=362\ pounds$

$3W_1=722\ pounds-362\ pounds=360\ pounds$

Which results in $W_1=\frac{360\ pounds}{3}=120\ pounds$

And we return to the first equation to have:

$W_2=361\ pounds-2W_1=361\ pounds-2(120\ pounds)=121\ pounds$