# Math riddle..help anyone?!

Hey everyone, My son has this math riddle and it’s driving me crazy! Can someone please show me how this is done? Here it goes…

A seesaw can balance with more than one weight on each side as long as the sum of the products of the weights on one side and their distances from the fulcrum is equal to the sum of the products of the weights on the other side and their distances from the fulcrum. Can you determine how much the duck and rabbit on this seesaw weigh from the following clues?
The sum of the four weights is 40 pounds.
The owl weighs 3 pounds
The chicken weighs 5 pounds.

(And theres a picture…ill do my best)

duck…owl…chicken…rabbit
2…7…^…9…4

the numbers under my poorly shown scale above represent how far from the center of the scale the animal is (and the rabbit is 4 away from the chicken and the duck is 2 away from the owl…i guess…)

As you can see , I’m lost. Can anyone help me??

You know that m[sub]duck[/sub]d[sub]duck[/sub] + m[sub]owl[/sub]d[sub]owl[/sub] = m[sub]chicken[/sub]d[sub]chicken[/sub] + m[sub]rabbit[/sub]d[sub]rabbit[/sub]. m is the mass of the animal, and d is the distance from the fulcrum.

We know all the distances, so we get 9m[sub]duck[/sub] + 7m[sub]owl[/sub] = 9m[sub]chicken[/sub] + 13m[sub]rabbit[/sub]. We also know two of the masses, so we have 9m[sub]duck[/sub] + 21 = 45 + 13m[sub]rabbit[/sub]. Lastly, we know that the duck and rabbit together weigh 32 pounds. So 9m[sub]duck[/sub] + 21 = 45 + 13(32 - m[sub]duck[/sub]). Or 22m[sub]duck[/sub] = 24 + 13*32. I get m[sub]duck[/sub] = 21 + 1/11. Check that.

Reaching deep into the dim mists of my memory.

d+o+c+r=40
o=3
c=5
so d+r+8=40
d+r=32, d=32-r

9d+7o=9c+13r
so 9d+21=45+13r
9d=13r+24
9(32-r)=13r+24
288-9r=13r+24
264=22r
r=12
d=20

ultrafilter , you were fine until you made a small arithmetical mistake.

Argatha has it, the duck is 20 lbs and the rabbit 12. I did it very slightly differently, treating it as a system of 2 equations in two unknowns, arriving at
1): D + R = 32
2): 9D - 13R = 24

13x1) + 2): 22D = 440 or D = 20 and so R = 12

What it seems your son is studying is the solution of systems of linear equations. Soon, he may be wandering into the well-ordered arena of matrices - not to be confused with The Matrix.

Wouldn’t be the first time. Non-Euclidean geometry? No problem. Galois theory? Piece of cake. Basic arithmetic? Can’t do it.

Heh. Well, I made three mistakes, but I caught them…
May I recommend the virtures of “substituting back in”?
You then find that the moment of each side comes out to 201, and that everything is somewhat sane.
A cigar for Agartha, but I’m more interested in that 20 pound duck you’ve got there…

What happened to the missing \$1?

MMmmmmmmm. Roast duck.

A 20 pound duck is pretty darn big.

burp