On Friday I posted this puzzle….

The other day my friend sent me this note:

‘I’ve changed the calibration dial on my bathroom scale, and so the readings are off by a consistent amount. When I am on the scale it reads 170 pounds, and when my wife is on it, it reads 130. When we stand on it together the scale reads 292 pounds. How should I adjust the scale?’

If you have not tried to solve it, have a go now. For everyone else, the answer is after the break.

When my friend and his wife are standing on the scale, the difference in the readings will show us her true weight, 292 – 170 = 122 pounds. So the scale is set 130 – 122 = 8 pounds too high.

Did you solve it?

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Yes, thanks for the puzzle!

I did it by adding the two true weights, getting 300, then taking the difference with 292 and getting 8 pounds. But then I had to do some thinking in my head to realize that 2*error – error = error. So I like your way better.

Yes I got it but not in the simple manner of the solution given.

I created a spreadsheet showing the sum of the two weights less; one pound; two pounds; three and so on until arriving at less eight.

Loved your way though. I imagine many went that same route.

Take the total of two people weighed together (including 1 offset) from the combined weights of two people weighed separately (including 2 offsets). The difference is 1 offset.

Great. Got a Maths one!

Do what any normal person does and adjust it when you’re not on the scales.

I dont get it, I got the 8 pounds offset on the total weight, but..

When the man is on the scale alone it reads 170 (this is including a offset of 8?)

so its real weight is 178 an when the woman is on it it reads 130 (with an offset

of also 8) real weight is 138. their combined weight is then 316, right?

then the scale should read 308 when they are both on it??

or are the separate scales without offset?

okay got it… offset is the other way! original weight is 162 and 122……duhh

kroketje, you’re going the wrong way. The man’s real weight is 162 (8 lbs. LESS than what the scale shows), and the woman’s real wieght is 122. So together they really weigh 284, which is 8 lbs. less than what the scale shows.

Oops. I didn’t see that you caught your own error.

I got it using the force.

Another solution. From argentina this time 😉

The combined reading should be 300.

But it reads 292.

So the difference between the two is the deviation. In this case:

300-292 = 8

😉

Reason: the scale always adds up only ONE deviation.

Simpler isn’t it?

That way to the solution was chosen by me, too. Only a single (cheesy) addition (difference is seen, not calculated), so it lasted only a few seconds.

This one was way below the belt! The wording implies that the readings of 170 and 130 pounds were obtained on the messed-up scale. When I added and subtracted to get 8 pounds, I assumed that the error increased with additional weight added to the scale. If this were the case, it would be impossible to correct the scale simply by adjusting the offset.

In other words, Aaaarrgh!

i was thinking in the same way..

“the readings are off by a consistent amount” is fairly unambiguous, isn’t it?

No. “Consistent” is not the same as “constant”. After all, if the scale could be assumed to always be a constant 8 pounds too high, the natural thing to do would be to adjust the empty reading down from 8 to 0; no fancy maths necessary. On the other hand, if it was *consistently* a 10% higher reading, you have a different puzzle altogether.

Since the readings are consistently wrong, I just devised the following equation and solved for x.

170 + x + 130 + x = 300 + x

Seemed the most obvious way of solving it 🙂

*= 292 + x

Yeap veli, that’s the ecuation of my calculus:

300-292 =8

Pablo.

In fact it’s

-300+292=-8

Yeah I solved it like veli

x=his weight

y=her weight

c=correction

x+c=170

y+c=130

x+y+c=292

(x+c)+(y+c)=x+y+2c=170+130=300

c=(x+y+2c)-(x+y+c)=300-292=8

so the weight adds 8 pounds

Your solution is clear and a proper application of algebra.

Nobody is solving the actual puzzle. The question posed was: “How should I adjust the scale?” The answer I came up with (in 0 seconds) was: you should adjust it to read whatever makes you happy. He even admits to having already done this, so clearly no further adjustment is necessary.

Right! But I think the answer should be “By changing the calibration dial again…the same way you messed it up.”

I agree, while I solved this in terms of the puzzle implied, the actual question is easily answered by just saying, adjust the dial with no one on it till it points to zero or other variations, no where does it imply you need to calculate the “error”. Would of been better to just ask how much the scale was off by.

“When my friend and his wife are standing on the scale, the difference in the readings will show us her true weight, 292 – 170 = 122 pounds. So the scale is set 130 – 122 = 8 pounds too high.” The solution provided is missing main point. Main point is when two people together or separately stand on the scale adjustment counted only once. So we can find true weight either of husband or wife by subtracting these two measurements. Real weight of wife is 292 – 170 = 122 pounds than the scale adjustment is set 130 – 122 = 8 pounds. Or real weight of husband is 292 – 130 = 162 pounds than the scale adjustment is set 170 – 162 = 8 pounds.

The question is, “How should I adjust the scale?” The answer is, “By turning the calibration dial, you idiot, just like last time.” However a better answer would be, “Stop playing cruel tricks on your wife, you bastard. And what a jerk you were at the end of it all, getting your wife to get on the scale with you and then turning it in math problem! She probably thought you were being romantic! I hope she makes you sleep on the couch.”

If you get of the scale, does it read 0 (zero) ? It should.

I was delighted when I posed this question to my kids at dinner and my 10-year-old son said, “Well, if you subtract the man’s weight of 170 from 292, you get 122, which must be the woman’s real weight, so the difference is 8 pounds.” QED in the mind of a boy genius.

a + x = 130

b + x = 170

a + b + x = 292

a + b + x – b – x = 292 – 170 = 122

a = 122

a + x -a = 130 -122 = 8

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