In Lewis Carrolls book The Looking Glass Alice encounters th

In Lewis Carroll\'s book \"The Looking Glass\", Alice encounters the twins Tweedledee and Tweedledum. This is what they say to each other about their weights...

Tweedledum says to Tweedledee: \"The sum of your weight and twice mine is 361 pounds.\"

Tweedledee says to Tweedledum: \"Contrawise, the sum of your weight and twice mine is 362 pounds.\"

How many of each weigh? Use a system to find out.

Tweedledee weighs  pounds and Tweedledum weighs  pounds.

Solution

Let x = Tweedledee\'s weight.
Let y = Tweedledum\'s weight.
So, according to Tweedledum, x + 2y = 361 Rewrite as: x = 361 - 2y and substitute in the equation below:
and according to Tweedledee, y + 2x = 362
After the substitution, we have:
y + 2(361 - 2y) = 362 Now, solving for y:
y + 722 - 4y = 362
-3y = -360

y = 120 lbs This is Tweedledum\'s weight, which is not too bad in lbs, but if it were in stones, he would definitely be obese.
x = 361 - 2y
x = 361 - 2(120)
x = 361 - 240
x = 121 lbs This is Tweedledee\'s weight and the same comment applies.
Check:
Tweedledum says, \"The sum of your weight and twice mine is 361\"
Since x is Tweedledee\'s weight, then we have:
x + 2y = 121 + 2(120) = 121 + 240 = 361 and, contrariwise, according to Tweedledee:
y + 2x = 120 + 2(121) = 120 + 242 = 362