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An man inspects every 36th egg for cracks and every 48th egg for weight. What is the fist egg he checks for both?

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3 Answers

Here you go Brian...
 
Since he checks every 36th egg for cracks and every 48th egg for weight let x = a multiple of 36 and let y = a multiple of 48.  for the two to happen together we know that 36x = 48y.
 
Then rearranging we know that x/y = 48/36.  Reducing the ratio of x/y = 4/3
 
So (36)(4) = (48)(3) = 144.  So the 1st egg checked for both would be egg 144.
And that will be the number you will can divide by 36 and 48. It calls Least Common Multiple (LCM).
Let's use prime factorization:

  36 = 2 × 2 ×             3 × 3
  48 = 2 × 2 × 2 × 2 × 3
          ↓     ↓     ↓    ↓    ↓     ↓
LCM = 2 × 2 × 2 × 2 × 3 × 3

LCM (36, 48) = 144

144th egg will be inspect for cracks and weight.

Comments

By FAR, the best way to solve the problem.
Hey Brian -- since they're eggs, think "dozens" ... crack-scan 3doz, 6doz, 9doz, 12doz
... wt-scan 4doz, 8doz, 12doz ==> intersect at 12 doz or 144th egg ... Regards, sir :)