Bacteriology/Food Science 324:
KEY TO THE SAMPLE INDICATED NUMBER
AND MPN PROBLEMS
to go along with Exercise 2 and Appendix F.2
in the 1999 edition of the lab manual

1. In each of the following, a food product was decimally diluted, and one ml from each dilution was inoculated into a tube of an all-purpose broth medium. After incubation, the tubes showing growth were marked with a +. State the indicated number of organisms per gram of food product in each of the following:
   
   
   1. 
      

      Dilution of the food	10–2	10–3	10–4	10–5
      Result	+	+	–	–

      
      

      At least one organism able to produce a population of cells in the medium (ultimately visible as growth) was present in the one ml inoculum from the 10^–3 dilution. Therefore, there were at least 1000 (or 1 X 10³) per gram of the original, undiluted food product. Likewise there were none ("less than 1") in the one ml inoculum from the 10^–4 dilution, so we can say there would have been less than 10,000 (or 1 X 10⁴) per gram of the original, undiluted food product. Therefore, the indicated number per gram of the food product would be equal to or greater than 1 X 10³ and less than 1 X 10⁴.

   2. 
      

      Dilution of the food	1/10	1/100	1/1000	1/10,000	1/100,000
      Result	+	+	–	+	–

      
      

      Switching the results for the 1/1000 and 1/10,000 dilutions (invoking "Phelp's Index") and using the same reasoning as in the above problem, the indicated number per gram of the food product would be equal to or greater than 1 X 10³ and less than 1 X 10⁴.

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2. One gram of food was blended with 9 ml of diluent. Three additional 1/10 dilutions were made. From each of these four serial dilutions of the food, tubes of an all-purpose broth medium were inoculated as shown in the table below. After incubation, the following results were obtained:
   
   

   Dilution of the food	10–1	10–2	10–3	10–4
   Amount of dilution inoculated into each of 3 tubes of broth	1.0 ml	1.0 ml	1.0 ml	1.0 ml	0.1 ml
   Number of tubes showing growth	3	3	3	2	0

   Using a 3-tube MPN table, determine the most probable number (MPN) of microorganisms per gram of the food.

   (Note that in the table above, the tubes in the last set were each inoculated with 0.1 ml of the 10^–4 dilution – which is of course equivalent to being inoculated with 1.0 ml of a 10^–5 dilution. The rule that we must have decimally decreasing amounts being inoculated into the tubes is maintained.)

   Choose 3-2-0 for your results. Using the 3-tube MPN table, 3-2-0 corresponds to 0.93. So, according to the table, there would be 0.93 microorganism (able to grow in the medium) per inoculum of the middle set of tubes – which received 1.0 ml of a 10^–4 dilution. Therefore, in the original, undiluted food, we would expect 10⁴ times as many organisms per gram, so the MPN per gram of the food would be 0.93 X 10⁴ or 9.3 X 10³.

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3. Five grams of food were blended with 45 ml of diluent. Three additional 1/10 dilutions were then made. From each of these four serial dilutions, one-tenth ml was inoculated into each of three tubes of an all-purpose broth medium. The following results were observed after incubation:
   
   

   Dilution of the food	10–1	10–2	10–3	10–4
   Amount of dilution inoculated into each of 3 tubes of broth	0.1 ml	0.1 ml	0.1 ml	0.1 ml
   Number of tubes showing growth	3	3	1	0

   Using a 3-tube MPN table, determine the MPN of microorganisms per gram of the food.

   (Note that we added the middle row of the above table for this key. Don't forget the effect of inoculum size on the results, and it was not figured into the top row which just indicates the dilution we made of the food itself, according to the text of the problem.)

   Choose 3-1-0 for your results. Using the 3-tube MPN table, 3-1-0 corresponds to 0.43. So, according to the table, there would be 0.43 microorganism (able to grow in the medium) per inoculum of the middle set of tubes – which received 0.1 ml of a 10^–3 dilution. This is equivalent to 1.0 ml of a 10⁴ dilution of the food. Therefore, the MPN per gram of the food would be 0.43 X 10⁴ or 4.3 X 10³.

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4. A sample of raw hamburger was divided aseptically, and weighed portions were added to flasks of appropriate amounts of pre-enrichment broth utilized in the FDA Salmonella isolation and identification procedure (Exp. 16). The amounts utilized are indicated in the table below. The entire FDA procedure for the enrichment, isolation and identification of Salmonella was done from each flask, and the number of flasks which ultimately yielded confirmed Salmonella is indicated below.
   

   Amount of hamburger added to each of three flasks of broth	50 g	5.0 g	0.5 g
   No. of flasks from which Salmonella was isolated	3	3	0

   Calculate the Salmonella count (i.e., the most probable number of Salmonella) per gram of the hamburger.

   Checking the table, 3-3-0 indicates an average of 2.4 organisms (in this case, Salmonella) were inoculated into each of the middle set of flasks – i.e., those inoculated with 5 grams of hamburger. If 2.4 were in 5 grams of the hamburger, this is equivalent to 0.48 being in 1 gram.