Mathematics in AFNR
Word Problems
2B. Depreciation
If a $500 gasoline powered generator loses 20 percent of its value each year, what is
the value of the generator at the end of 3 years?
Formula
Answer:
N = 500(.80)3
$256.00
3B. Ration Calculations using a Pearson Square
A Pearson Square is used to solve mixture problems. Algebraically, this is known
as a system of linear equations.
% in component A
(cost of A)
parts of component A
Desired % or
cost
% in component B
(cost of B)
parts of component B
sum of the parts of component A and B
The Diamond Bar Feed Store sells a grain mixture for donkey feed. If cracked corn
sells for 25 cents per pound and crimped oats sells for 20 cents a pound, what
amount of corn and oats should be mixed so that a 50 pound bag of mixture would
sell for $11.00?
Solution:
1. First find the desired price per pound. $11/50 lbs. = 22 cents per pound
25 cents/1 lb.
cracked corn
22 –
20 = 2 parts cracked corn
Desired cost
22 cents/lb.
mixture
20 cents/1 lb.
crimped oats
25 – 22 = 3 parts crimped oats
Total = 5 parts mixture
Pearson Square continued.
Corn: 5
2
 50 lbs = 20 lbs. of cracked corn
3
5
 50 lbs = 30 lbs. or crimped oats
Oats:
Algebraically, using system of linear equations.
Let x = lbs. of needed cracked corn
Let y = lbs of needed crimped oats
x + y = 50
.25x + .20y = 11
Solve for x and y
5A. Exponential Growth of Bacteria
A certain bacteria population doubles in size every 12 hours. By how much will it
grow in 2 days?
Let t = 48 hours (2 days)
Let d = 12 hours
N = No  248/12 = No  24 = 16 No
Answer: Therefore the population grows by a factor of 16 in 2 days.
6A. Calibration of pesticides/herbicides
Farmer Brown finished spraying a field with herbicide using his 500 gallon capacity
sprayer. He was spraying the chemical at the rate of 1 quart per acre with a total
spray volume of 10 gallons per acre. He has 200 gallons of spray left in his tank.
The next field that he wishes to spray will use the same chemical but at the rate of
1.5 quarts per acre with a total spray volume of 10 gallons per acre. How much
chemical will need to be added to make a full tank of spray using what is left in the
tank and adding to it to make a full tank load?
7A. Fertilizer application rates
Fertilizer analysis represents the proportion in which the three standard ingredients
nitrogen (N), phosphoric acid (P) and potash (K) are present in a mixture. The
nutrients are always given in the same order N-P-K.
A fertilizer has an analysis of 20-12-5. Explain.
Answer:
20 parts nitrogen
12 parts phosphoric acid
5 parts potash
}
This means, that every 100 pounds of fertilizer would
contain 37 pounds of nutrients (N-P-K).
How many pounds of 20-12-5 fertilizer should be purchased to apply 5 pounds of
actual nitrogen to 1000 square feet of lawn?
Pounds desired divided by percent of nutrient = pounds required.
5 lbs.  .20 (percentage of nitrogen) = 25 lbs.
Answer:
25 lbs of 20 – 12 – 5 fertilizer
8B. Ohm’s Law
Direct Variation
The electrical resistance in ohms (  ) of a wire varies directly as its length. If a
wire 110 cm has a resistance of 7.5 , what length wire will have resistance of 12 ?
Let l = the required length in centimeters. Since the ratio is constant,
110 = 7.5 l
Solve for l
Answer:
Therefore, the wire’s length is 176 cm.
Inverse Variation
By Ohm’s Law, the current flowing in a wire is inversely proportional to the
resistance of the wire. If the current is 5 amperes (A) when the resistance is 24
ohms (), for what resistance will the current be 8A?
I=
E
R
5= E
24
Solve for E; E = 120 Volts
8=
120
R
Solve for R
Answer: Therefore, the resistance is 15.