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Pearson’s Square

Pearson’s Square. Balancing Feed Rations. Why Balance Rations?. Maintain animal health Optimum animal production Reasonable production cost for the farm manager. Maintain Animal Health. Why maintain animal health in horses?

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Pearson’s Square

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  1. Pearson’s Square Balancing Feed Rations

  2. Why Balance Rations? • Maintain animal health • Optimum animal production • Reasonable production cost for the farm manager

  3. Maintain Animal Health • Why maintain animal health in horses? • So that the horse can have a balanced diet that can maintain the horse’s weight and energy supply.

  4. Optimum Animal Production • Helps give protein and nutrient requirements needed for different stages of production. • Maintenance • Lactation • Gestation • Growth • Yearling • Long-yearling • 2 year old • Mature (4+ years)

  5. Production Cost for Farm Manager • How does balancing a feed ration affect production cost? (better or worse?) • Better • It keeps from wasting feed

  6. Math Terms Involved • Diagonal • A square with lines connecting the opposite corners • Percent • 1% of a number means 1 hundredth of a number or .01 • 6% means six hundredths or .06 • Pound • Weight of an object • Lb, # • Systems of Equations • Two or more equation in two or more variables to be solved simultaneously • Ratio • The comparison of two numbers by division

  7. Nutrient Concentrations

  8. Feed Compositions

  9. Sample Problem • 2,000 pounds of feed is needed to feed a pregnant mare. A feeding standard table shows that a 10% crude protein ration is needed. Corn and soybean meal are selected as feeds. A feed composition table shows that corn has 9% and soybean meal has 45% crude protein on as-fed basis. How much corn and soybean meal need to be mixed together for 2,000 pounds of feed?

  10. Sample Problem • What’s important? • 2,000 pounds of feed needed • 10% crude protein needed • Corn contains 9% protein • Soybean meal contains 45% protein

  11. Pearson’s Square • Step 1 • Draw a square with lines connecting the opposite corners. Write the percent of crude protein needed (10) in the center of the square where the lines cross.

  12. Pearson’s Square • Step 2 • Write the feeds to be used and their crude protein percents at the left hand corners of the square.

  13. Pearson’s Square • Step 3 • Subtract the smaller number from the larger number along the diagonal lines. Write the difference at the opposite end of the diagonals.

  14. Pearson’s Square • Step 3—check • The sum of the numbers on the right equals the difference in the numbers on the left.

  15. Pearson’s Square • Step 4 • Divide the parts of each feed by the total parts to find the percent of each feed in the ration. • Corn: (35/36) x 100 = 97% • Soybean: (1/36) x 100 = 3%

  16. Pearson’s Square • Step 5 • It is known that 2,000 pounds of the mixture is needed. Thus, the amount of corn needed is 1,940 pound. This is found by multiplying the percent of corn in the mix by the total pounds of the mix. • 2,000 x 0.97 = 1,940 pounds

  17. Pearson’s Square • Step 5 • The amount of soybean meal needed 60 pounds. This is found by multiplying the percent of soybean meal in the mix by the total pounds of the mis • 2,000 x 0.03 = 60 pounds

  18. Pearson’s Square • Step 6 • Check the mix to make sure the protein needed is met. Multiply the pounds of corn by the percent of protein in the corn (1,940 x 0.09 = 174.6). Multiply the pounds of soybean meal by the percent of protein in the soybean meal (60 x 0.45 = 27). Add the pounds of the protein together. Divide by the total weight of the mix.

  19. Pearson’s Square • Step 6 • 174.6 + 27 = 201.6 • (201.6 / 2000) x 100 = 10%

  20. Algebraic Solution

  21. Algebraic Solution • X + Y = 2,000 • .09X + .45 Y = .10(2000) • Solve for a variable, in this case X: • X + Y = 2,ooo -Y -Y • X = 2,000 - Y

  22. Algebraic Solution • Solve for Y • .09(2000 – Y) + .45Y = 200 • Substitute X with X=(2,000 – Y) • 180 - .09Y + .45Y = 200

  23. Algebraic Solution • 180 + .36Y = 200 -180 -180 • .36Y = 20 (Divide both sides by .36) • Y= 55.6 pounds of soybean

  24. Algebraic Solution • Solve for X • Substitute the value of Y into the first equation • X + 55.6 = 2,000 -55.6 -55.6 • X = 1944.4 pounds of corn

  25. Algebraic Solution • Check • X = 1944.4 pounds of corn • Y = 55.6 pounds of soybean • Substitute to check • X + Y = 2,000 • 1944.4 + 55.6 = 2,000

  26. Sample Problem • 2,000 pounds of feed is needed to feed a lactating mare. A feeding standard table shows that a 12.5% crude protein ration is needed. Oats and linseed meal are selected as feeds. A feed composition table shows that oats has 12% and Linseed meal has 38% crude protein on as-fed basis. How much oats and linseed meal need to be mixed together for 2,000 pounds of feed?

  27. Sample Problems • 2,000 pounds of feed is needed to feed a weanling. A feeding standard table shows that a 14.5% crude protein ration is needed. Mixed sweet feed and a commercial protein supplement are selected as feeds. How much mixed sweet feed and commercial protein supplement need to be mixed together for 2,000 pounds of feed?

  28. Sample Problem • 2,000 pounds of feed is needed to feed a yearling. How much sorghum and soybean meal need to be mixed together for 2,000 pounds of feed?

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