Basic Math Operations - Mathematics and Statistics for the Environment - page 50

■ EXAMPLE 2.26
Problem: For the primary influent flow, the following composite-sampled solids concentrations
were recorded for the week:

Monday 310 mg/L SS

Tuesday 322 mg/L SS

Wednesday 305 mg/L SS

Thursday 326 mg/L SS

Friday 313 mg/L SS

Saturday 310 mg/L SS

Sunday 320 mg/L SS

Total 2206 mg/L SS

What is the average SS?

Solution:

Sumofall measurements
Number of

AverageSS =

measurements used
mg/L SS

2206

= = 315.1 mg/L SS

7

2.8 R ATIO
A ratio is the established relationship between two numbers; it is simply one number divided by
another number. For example, if someone says, “I'll give you four to one the Redskins over the
Cowboys in the Super Bowl,” what does that person mean? Four to one, or 4:1, is a ratio. If someone
gives you four to one, it's his or her $4 to your $1. As another more pertinent example, if an aver-
age of 3 cubic feet (ft 3 ) of screenings are removed from each million gallons (MG) of wastewater
treated, the ratio of screenings removed to treated wastewater is 3:1. Ratios are normally written
using a colon (such as 2:1) or as a fraction (such as 2/1). When working with ratios, the following
key points are important to remember.

• One place where fractions are used in calculations is when ratios are used, such as calculat-
ing solutions.
• A ratio is usually stated in the form A is to B as C is to D, which can be written as two
fractions that are equal to each other:

A
B

C
D

=

• Cross-multiplying solves ratio problems; that is, we multiply the left numerator (A) by the
right denominator (D) and say that the product is equal to the left denominator (B) times
the right numerator (C):

A × D = B × C (or, AD = BC)

• If one of the four items is unknown, dividing the two known items that are multiplied
together by the known item that is multiplied by the unknown solves the ratio. For example,
if 2 lb of alum are needed to treat 500 gal of water, how many pounds of alum will we need