# Sample Math Problems for Microbiology

Remember, all these calculations for calculating microbe per unit volume from the results of a plate count depend on this equation:

CFU/standard unit volume = no. of colonies x dil’n factor x standard unit volume/aliquot plated

The answers to the problems can be found at the bottom of the page.

PROBLEMS: (Note that they get more challenging as you work your way through them.)

1. 0.1 mL of urine plated out on nutrient agar. After incubation at 37C, 279 colonies appeared. Give the CFU/mL. How many CFU are there per 100 mL?
2. A sample was diluted by placing a 0.1 mL aliquot into 0.9 mL of diluent, and 1 mL of this dilution was pour-plated. After incubation, 217 colonies appeared. What is the CFU/mL in the original specimen?
3. A culture was diluted by adding a 0.1 mL aliquot to 0.9 mL water. Then, 0.1 mL of this dilution was plated out, yielding 73 colonies. Calculate the CFU/100 mL in the original culture.
4. A dilution of a bacterial suspension was prepared by adding 100 lambdas of the suspension to 9.9 mL of sterile physiological saline (PSS). 100 of this dilution was plated out, yielding 27 colonies. Give the CFU/mL in the original culture.
5. A serial dilution was prepared by adding 0.1 mL to 9.9 mL, and 0.1 of that to 9.9 mL of fresh diluent. Then, 0.1 mL of the last dilution was spread. Later, 561 colonies were counted. What was the original CFU/mL?
6. 200 µL of milk was mixed with 9.8 mL diluent, and 10 lambdas of the dilution were pour-plated. If there were 141 colonies on the plate, what was the original CFU/mL in the milk?
7. 250 mL of drinking water was passed through a millipore filter, and the membrane was layered on a pad supplied with on m-Endo MF medium. 21 red colonies formed. What was the coliform/100 mL? Does this drinking water meet the standards for drinking water? Using this protocol, what would the largest number of coliform permitted and still have the water “safe for consumption?”
8. 10 µL of a phage lysate suspension were added to 9.99 mL diluent, 10 µL of that added to 9.99 mL fresh diluent. Then 10 µL of this last dilution plated with indicator bacteria. 207 plaques appeared following incubation. What was the titer of the original lysate (phage/mL)?
9. 0.73 gm of hamburger was suspended in 7.3 mL of diluent, 0.1 mL of the suspension diluted into 9.9 mL diluent, 0.1 of that into 0.9 mL diluent, and 0.2 mL of this last dilution was pour plated. 422 colonies formed. What was the CFU/g in the meat? Does this hamburger meet the standards for wholesome meat?
10. A 1 cm square surface was swabbed with a moistened sterile cotton swab, and the swab was suspended in 2 mL of sterile water and vortexed to suspend swabbed bacteria. 10 lambdas of this suspension was added to 9.99 mL diluent, and 20 lambdas were pour plated, and 106 colones appeared. What was the CFU/sq.cm on the surface?
11. A package of yeast (7.39 g) was suspended into 100 mL dH2O. This was serially diluted by transferring 0.1 aliquots successively to 9.9 dilution blanks three times in secession. 0.1 and 0.2 mL aliquots were spread on 2% glucose nutrient agar. Colonies appeared as follows: 0.1 plate: 179, 0.2 plate: 321. How many yeast were there originally in the package? How many yeast are there in a gram? How many picograms does a single yeast cell weigh?

Here are the answers to these problems:

1. a: 2,790/mL, b: 279,000/100 mL.
2. 2,170 CFU/mL.
3. 7.3 x 105 CFU/100mL.
4. 27,000 CFU/mL.
5. 5.61 x 107 CFU/mL.
6. 705,000 CFU/mL.
7. a: 8.4 coliform/100 mL, b: No it is not safe to drink, c: 25 colonies.
8. 2.07 x 1010.
9. 2.11 x 107. Yes, it is (barely) below the maximum permissible bacterial load,
10. 1.06 x 107/sq. cm,
11. a) 1.7 x 1011/package, b) 2.3 x 106/gram, c) 44 picograms/yeast cell.