**Garden Math Sample Problems and Calculations**

PSS 123 Garden Flowers

Dr. Leonard Perry, Univ. Vermont

These adaptations of problems from real life should help you with the
homework
assignment you'll submit for grading and credit. You should save
and print out the **Table
of Equivalents** which you'll find necessary here, and useful throughout
your future gardening, whether at home or professionally.

A couple other hints to make life easier: break the work into parts, and use ratios. For example with parts, if asked to convert mg/l to oz/gal, first covert the mg to oz, and then the L to gal. For ratios, set up the problem such as 1/3=?/6, then cross multiply so 6=3x, then divide each side by 3 giving 2=x.

**1. The edge of a circular flower bed, 220 ft in diameter, needs mulch.
How many cubic yards (yd ^{3}) of mulch do you need if you want
the mulch to cover 3 ft in from the edge to a depth of 2.5 inches, all
the way around?**

Diameter = 220 ft

radius = 110 ft.

pi = 3.142

Area of a circle = pi x r^{2}

Area of total bed = 3.142 x (110)^{2} = 38018.2 ft^{2}

Area of inside bed = 3.142 x (110-3)^{2} = 35972.8 ft^{2}

Area of ring needing mulch = 38018.2 - 35972.8 = 2045.4 ft^{2}

Volume of ring (2.5 inches deep = 0.208 ft) = 2045.4 x 0.208 = 425.4
ft^{3}

Convert cubic feet to cubic yards à
1 yd^{3} = 27 ft^{3} so 1 ft^{3 }= 0.037 yd^{3}

425.4 x 0.037 = 15.7 yd^{3} = 16 yd^{3}

OR

1 yd^{3} = 325 ft^{2} to 1" deep

__325 ft ^{2 }__

1 yd

325x = 2045 x = 6.29
6.29 x 2.5" = 15.75 yd^{3} = 16 yd^{3}

**2. You are going to plant a kidney shaped bed with annuals, with
each plant 1 ft from the next. The bed width measurements, which were taken
every 10 feet, are 11 ft, 13 ft, 5 ft, and 17 ft. Approximately how many
annuals will you need to fill the bed?**

Area = (add the widths) multiply times feet between each width measurement (you're basically adding up several rectangles, granted the bed edges curve, but the extra plants make up for those on the ends)

Area = (17 + 5 + 13 + 11) x 10 = 460 ft which at 1 ft apart (one sq ft per plant) means 460 annuals

**3. How many bags of potting soil would you need to fill 5 very large
planters that take 1.75 bushels of potting medium each? Each bag of potting
medium is about 3 cubic feet.**

1.75 bushels x 5 planters = 8.75 bushels needed

__1 bushel__ __8.75
bushels__

1.25 ft^{3} =
x

x = 11 ft^{3}

__11 ft ^{3}__ = 4 bags

3 ft

**4. You read a fertilizer recommendation for flower gardens and want
to try it in your own. Your garden area is 1545 square feet and the recommendation
is for 2050 pounds per hectare. How much fertilizer will you need?**

To convert square ft to acres à
multiply by 2.296 x 10^{-5}

1545 ft^{2} x (2.296 x 10^{-5}) = 0.035 acres

To convert acres to hecatres
__1 acre __ = __0.035__

0.4047 ha
x
x = 0.014 ha

__2050 lbs__ = __x__

1 ha
0.014 ha
x = 28.7 lbs (= 29 lbs)

**5. How much of ProGro, a 5-3-4 organic fertilizer, do you need to
get the same amount of phosphorus (P _{2}0_{5}) as if you
were using 15 pounds of a 15-10-10 chemical fertilizer?**

5-3-4 fertilizer = 3% P_{2}0_{5}

15-10-10 fertilizer = 10% P_{2}0_{5} à
15 lbs x 10% = 1.5 lbs of P_{2}0_{5}

3% times __x__ lbs in 5-3-4 = 1.5 lbs P_{2}0_{5}
in 15-10-10 x = 50 lbs
P_{2}0_{5}

**6. A gardener applies a dry 20-10-20 fertilizer to her flower beds,
using 2 pounds of potassium (K _{2}0) per 1000 square feet, 2 times
a year. If a 50 lb bag of this fertilizer costs $9.50, how much is this
gardener paying a year for this application?**

20-10-20 fert. = 20% K_{2}0 à
20% x = 2 lbs x = 10 lbs
20-10-20 times twice a year = 20 lbs 20-10-20

__50__ = __20__

9.50 x
50x = 190
x = $3.80

**7. You only have access to measuring devices that are in mL and liters
but you know you need 4 teaspoons per gallon of a liquid fertilizer. How
many mL per liter is that?**

1 L = 0.264 gal 1 tsp = 5 mL à 4 tsp = 20 mL

__x mL __ = __20
mL__

0.264 gal 1 gal
x = 20 * 0.264 = 5.28 mL/L

**8. Your dry fertilizer recommendation calls for 7 ounces per gallon,
or how many grams per liter is that?**

1 oz = 28.35 g à 7 oz = 198.45 g 1 L = 0.264 gal

__198.45 g__ = __x
g__

1 gal
0.264 gal
x = 198.45 * 0.264 = 52.39 g/L

**9. Your recipe for potting mix calls for 4 pounds per cubic yard
of one of the fertilizer ingredients. You are only making 4 1/2 cubic feet.
How many grams of this ingredient do you need to add?**

1 lb = 453.6 g à 4 lbs = 1814.4
g 1 ft^{3} = 0.037 yd^{3} à
4.5 ft^{3} = 0.1665 yd^{3}

__1814.4 g__ = __x
g__

1 yd^{3 }
0.1665 yd^{3 }
x = 302.09 g / 4.5 ft^{3}

OR __1814.4 g__ = __x
g__

1 yd^{3}
0.037
x = 67 à 67 * 4.5 = 301.5 g/ 4.5 ft^{3}

**10. You have a pesticide sprayer that holds 70 quarts but your directions
for a botanical pesticide are to mix it at a rate of 8 fluid ounces per
100 gallons. How much do you need to mix for your sprayer?**

__1 gal __ = __x
gal__

4 qt.
70 qt.
4x = 70
x = 17.5 gal

__8 fl oz __ = __x
fl oz__

100 gal 17.5 gal
100x = 140 x = 1.4 fl oz.

**11. You see a recommendation for a horticultural oil spray for mildew
of 12ml/L. How many Tablespoons (Tbsp)/gallon is this? **
3.785L in gal

__12ml__ = __ x ml__
x=45ml/gal

1L
3.785L

__5ml __ = __45ml __
x=9tsp/gal=3Tbsp/gal (3tsp=1Tbsp)

1tsp x tsp

**12. You begin work in a greenhouse and are asked to make up
a 100ppm (part per million) nitrogen (N) solution of fertilizer using 20-10-20.
How many ounces of fertilizer will you add for 100 gallons to get the 100ppm
N?**

1ppm=1 mg/L so 100ppm=100mg of N needed/L but the fertilizer is 20%N, so

__100mg fert__ = __x mg fer__t
x=500mg fertilizer needed/L

20mg N
100mg N

__500mg__ = __x mg __
x=1892.5mg=1.89g/gal times 100 gal = 189g/100gal

1 L
3.785L (gal)

__28.35g__ = __189g __
x=6.7oz/100 gal

1 oz
x oz

**13. How much actual P is in a 80lb bag of 15-30-15 fertilizer?**

as you probably know, the numbers stand for %N-%P_{2}0_{5}-%K_{2}0,
so you have to convert to actual P and K

__100lbs fert__ = __80lbs fert__
x=24lbs P_{2}0_{5} or alternately 30% times 80= 24

30 lbs P_{2}0_{5 }
x lbs P_{2}0_{5}

from Equivalents table you see that P x 2.3 = P_{2}0_{5}
so P_{2}0_{5} divided by 2.3 = P, or 24/2.3= 10.4 lbs P
in the 80 lb bag

Appreciation is expressed to Andrea Luchini for help in preparation of these samples.

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