Solving for the Unknown - Basic Mathematics for Water and Wastewater Operators - page 126

SETTING UP EQUATIONS
The equations discussed to this point were expressed in algebraic language. It is
important to learn how to set up an equation by translating a sentence into an equa-
tion (into algebraic language) and then solving this equation. To set up an equation
properly, the following suggestions and examples should help:
1. Always read the statement of the problem carefully.
2. Select the unknown number and represent it by some letter. If more than
one unknown quantity exists in the problem, try to represent those numbers
in terms of the same letter—that is, in terms of one quantity.
3. Develop the equation using the letter or letters selected and then solve.
■ Example 8.36
Problem: One number is eight more than another. The larger number is two less than
three times the smaller. What are the two numbers?
Solution : Let n represent the small number. Then n + 8 must represent the larger
number.
n + 8 = 3 n - 2
n = 5 (small number)
n + 8 = 13 (large number)
■ Example 8.37
Problem: If five times the sum of a number and six is increased by three, the result
is two less than ten times the number. Find the number.
Solution : Let n represent the number.
5( n + 6) + 3 = 10 n - 2
n = 5
■ Example 8.38
Problem: If 2 x + 5 = 10, solve for x .
Solution:
2 x + 5 = 10
2 x = 5
x = 5/2 = 2.5