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

By setting up a system of linear equations based on the statements from Tweedledum and Tweedledee, we find that Tweedledum weighs 120 pounds and Tweedledee weighs 121 pounds.

Step-by-step explanation:

In the puzzles presented by Lewis Carroll in Through the Looking Glass, Tweedledum and Tweedledee provide clues to their respective weights through a pair of equations. To find the weights of Tweedledum and Tweedledee, we can set up a system of linear equations using the given statements:

• 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."

Let's define the variables to solve this problem:

• Let d be the weight of Tweedledum.
• Let e be the weight of Tweedledee.

Now, we can translate the clues into equations:

1. e + 2d = 361
2. d + 2e = 362

To solve these equations, we can use either substitution or elimination. We'll use elimination in this case.

Multiply both sides of the first equation by 2, yielding 2e + 4d = 722.

Rewrite the second equation for clarity: d + 2e = 362.

Subtract the second equation from the first: (2e + 4d) - (d + 2e) = 722 - 362, which simplifies to 3d = 360.

Dividing both sides by 3 gives us the weight of Tweedledum, d = 120 pounds.

We will now substitute d = 120 back into one of our original equations, such as e + 2(120) = 361, which simplifies to e + 240 = 361. Subtracting 240 from both sides gives us the weight of Tweedledee, e = 121 pounds.

Therefore, the weights of Tweedledum and Tweedledee are 120 pounds and 121 pounds, respectively.

Answer 2

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=(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`