Homework Module 1: Day 2

The list below uses certain symbols or symbol combinations as variables to represent certain quantities concerning a particular high school.  For example, C stands for the number of classes each student takes at that high school; G₉ stands for the number of 9th grade girls at the school.

You may want to think of some numerical values as representing the average for the appropriate group of students.

C	the number of classes taken by each student	5
G9	the number of 9th grade girls	230
B9	the number of 9th grade boys	246
G10	the number of 10th grade girls	215
B10	the number of 10th grade boys	213
G11	the number of 11th grade girls	189
B11	the number of 11th grade boys	198
G12	the number of 12th grade girls	178
B12	the number of 12th grade boys	183
Hm	the number of minutes each student spends on math homework each night	27
Ho	the number of minutes each student spends on homework other than math each night	52
M	the number of minutes in each class	50
D	the number of class days a year	180
LG	the number of hours a week each girl listens to music	18
LB	the number of hours a week each boy listens to music	15

Using the symbols above, it is possible to write many different algebraic expressions.   Although you can always substitute numbers and do the arithmetic, most of these expressions have no real meaning in the situation.

For example, consider the expression DL_G .  Certainly you can multiply "the number of days a year" (180) by "the number of hours a week each girl listens to music" (18), but the product you get (3,240) doesn't have any interpretation in terms of the problem.  In other words DL_G doesn't really mean anything.

However some expressions do have a meaning.  For example, in the expression H_m + H_o, in each term represents part of a students homework time.  The sum represents the total time each student spends on homework.  So the expression H_m + H_o is meaningful in the situation.

The phrase "the total number of minutes each student spends on homework each night" is a concise way to describe the number represented by H_m + H_o.  We will call this concise description the summary phrase for the expression.

The list above tells us that each student spends 27 minutes on math homework, so H_m = 27, and that each student spends 52 minutes on other homework, so H_o = 52.

Therefore, H_m + H_o = 27 + 52 = 79, so each student spends 79 minutes a night on homework.  But even if the numbers were different, H_m + H_o would still represent the number of minutes each student spends on homework each night.

 

Your Task

Your task is to come up with as many meaningful algebraic expressions as you can, using the symbols above. For each expression, do the following:

• Write the expression.
• Explain what the expression means, using a summary phrase.
• Give the numerical value of the expression, based on the values of the individual variables given in the chart.

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