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.