Page 80 - Calculating Agriculture Cover 20191124 STUDENT - A

6-2 Equations and Formulas CH 6]

THE FORMULA

In Business and the agricultural sciences, much use is made of the formula. For example, a silo requires a
circular foundation. To calculate the area of that foundation, the formula for the area of any circle would be
2
2
used, and that formula is: Area = pi  radius  radius, A = π  r , or simply A = π r . Here are some real-
life problems that can be solved by using FORMULAS.

1. How much should I save from each paycheck to have enough money to purchase a
pickup truck?
2. How many tons of fertilizer should be applied to a field of soybeans?
3. How long will it take to haul sugar beets from the farm to the processing plant?
4. How many shares should be purchased to increase the portfolio value by 10%?

Advantages of the Formula

If a truck hauling produce travels at the rate of 40 miles per hour for 3 hours, the distance covered is (40
mph x 3h =) 120 miles. What this demonstrates is that the distance traveled is calculated using the equation:

d = rt.

The distance traveled will equal the product of the average rate and the time required for the trip. The
use of symbols and letters may be used to reduce the number of words needed to express the rule or
relationship; the formula. In this formula d stand for the distance, r represents the average rate (speed) of
travel, and let t represents the time. Such an equation, as d = rt, in which the variables (letters/symbols) are
used to express a rule, principal or relationship, is called a formula; it can also be called an equation.
Consider another problem. If all the numbers from 1 to 100 are added together, what will be their sum?
To obtain this sum you would add 1 and 2 and 3 and 4, etc., up to 100. However, a rule (formula) has been
developed to save much time and labor in this type of problem – a problem for depreciation of assets or
statistical analysis. The rule is: to obtain the sum add the first and last terms (1 and 100), multiply by the
number of terms, and then divide by 2. Using letters as symbols, the formula for this is:

n(a +l)
S = ———
2
Where S = sum, a = first term, l = last term and n = number of terms. As such this formula

n(a +l)
S = ——— becomes,
2

100(1 + 100) 100 (101) 10100
S = —————— = ———— = ——— = 5050
2 2 2

Use this formula to find the sum of numbers from 1 to 10 and then check with adding each digit from 1
to 10.

Why do we use formulas to solve problems?
1. Formulas are easier to remember in long statements.
2. Formulas are short and simple.
3. Formulas save time and work.

Writing Formulas from Verbal Statements.
Using letters to represent each of the values, a formula can be written which express a relationship
between numbers.

Example A: Write a formula for the number of inches ( I ) in t feet.

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