List of Formulas Inveractive Anglish Programing Types of Story Problems Examples of Story Problems Class II gross pay

# Class I - Rate Equation Problems

```Class I contains all of the problems with the basic
rate formulas of the form
a X b = c
For example:
rate X time = distance
rate X time = wage
rate X value = tax
Occasionally, multiplication may be replaced by division.  As in
portion / whole = fraction
and the equation may be more complex as in
rate1 X time1 + rate2 X time2 = wage
Some problems will have auxiliary formula's  with addition or subtraction as the operator as in
numberapples + numberpears = numberfruit```
A sample of the Class I problems from simple to complex follows:
Example 1: Joan works a 40 hour week at \$5.40 an hour. John works 32 hours for \$6.80 an hour. Jane earns \$6.25 per hour for 37.50 hours. What is their gross pay?
Example 2: Mary had to work 6.5 hours of overtime. Mark worked 5 hours of overtime and Martin worked 8. They all worked a normal 40 hour. Mary normally earns \$5.50 and hour, Mark \$4.75 and Martin \$6.00. For overtime, Mary got \$7.60, Mark got \$6.85, and Martin got \$8.10 an. What is the XYZ payroll?
Example 3: Mary got 8 question wrong on a 35 question quiz. What was her percent right on the quiz?
Example 4: A department store takes an item that costs \$32.50 at wholesale and retails it for \$50. What is the percent of the mark up?
Example 5: A coal mine yields 460 tons of coal every two days. How much coal is produced in five days?
Example 6: Mary does a job in 6 days while Sam does it in 8 days. How long does it take them to do the job together?
Example 7: Two boats took 3 hours to travel 129 miles in opposite directions. One boat travels 9 mph faster than the other. How far did each boat travel?
Most story problems are based on one or more standard equation. An important first step in solving these problems is to identify the equations needed. This is easily accomplished by selecting the equation that has the same elements as stated in the problem. Frequently, the equations are so obvious as not to be stated in the text books. For example:
```        total = number right + number wrong.
Or they are known in a very general form:
the total is equal to the sum of the parts.```
Many Class I problems consists of single equations that can be solved directly from the values given in the problem. Others consists of problems that have two or more simple algebraic expressions. The solution of one expressions determines a value needed for the solution of the second expression. The second expression produces the answer. Problems in this class contain statements which have a fact in common. However, the common fact is not specified and must be calculated. For example:
```        John missed 5 problems on his math quiz.  If there were 25 problems
total, what was his per cent correct?```
The problem asks for the percent correct, but the number of missed problems and the total number of problems is given. Therefore the formula
```        total = number correct + number missed.
must be solved for
number correct = total - number missed.```
first. This formula is then used to calculate the number correct which is used in a second formula to calculate the per cent correct.
`        (number correct / total) X 100 = per cent correct.`
Some problems use the same equation for both expressions. The first use is to calculate a value needed for the second use.
The third subclass of Class I problems requires a two dimensional tabular structure. Two equations are involved. One equation for each dimension.

Class II problems use relational equations.