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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?

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

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David S. | Wise Math TutorWise Math Tutor
5.0 5.0 (60 lesson ratings) (60)
1
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.
Nataliya D. | Patient and effective tutor for your most difficult subject.Patient and effective tutor for your mos...
1
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.
Brad M. | Summer Online Finance Specialist: WACC NPV DCF TVM YTMSummer Online Finance Specialist: WACC ...
4.9 4.9 (233 lesson ratings) (233)
0
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 :)