Over a period of a week, the 4 people in Group C ran a total of 27 miles, while the 6 people in Group D ran a total of 39 miles. On average, who ran more miles

Question

-an individual in  Group C or an individual in Group D?

 

I need these informations below:

Represent each group with ratios:

Write inequality to represent the answer of the question:

Answer the question in a sentence:

 

Answer 1

If you read the question very carefully, it asks you to compare the average number of miles per day for individuals in Group C versus individuals in Group D.

It does not ask for individual numbers; it asks us to compare group averages.  On average, Group C ran (27 miles / 4 people) and, on average, Group D ran (39 miles / 6 people).  That is simply comparing 27/4 to 39/6, right?  So, which is more miles per person?

Well, most people look at that and don't immediately know which is larger.  That's why a common denominator or a representation as a decimal is very helpful.  (note:  I taught fractions to a very experienced mechanic who could tell immediately whether 2/3 was bigger than 5/8, but I told him that the typical student needed the math solution).
 
So, keeping everything in ratios (fractions) and using 12 as a common denominator, we are comparing:
       27/4   ??    39/6
        81/12   ??    78/12
          81/12   >  78/12          (is this two steps, or what? !!)
  On average, individuals in Group C ran more miles per day than individuals in Group D.

Now, if you want to calculate specific averages, or use decimals or cross-multiply fractions or other operations, go ahead and spend the extra time.

Answer 2

The question asks for a comparison of the average miles completed by each group. 

The question asks to represent each group's average with a ratio. 

Lastly, the question asks for an inequality and written statement to represent the answer to the question.

 

 

The formula for averages is:  Total divided by number of things (i.e., people);

Total/# of people. 

 

 

 

Plugging in your values, each group's ratio is represented by: 

 

Group C--27 miles/4 people  (27/4).........................dividing you get the unit rate of 6.75 miles/per person

Group D--39 miles/6 people  (39/6).........................dividing you get the unit rate of 6.50 miles/per person

 

 

 

You can write your inequality using the ratio or decimal values:

27/4  >  39/6   or    6.75  >  6.50

 

 

Your written statement would explain that:

Group C ran an average of 6.75 miles per person, which is more than Group D's average of 6.50 miles per person. 

Answer 3

Ratios:

 

Group C: 27/4

 

Group D: 39/6

 

This problem requires you to divide in order to get the average total mile ran by each group.

 

Let X = total miles

 

4X=27

---  ---

4     4

 

X=6 r 3/4 =6.75

 

6X = 39

---    ---

6        6

 

X=6 r 3/6 = 6.50

 

Therefore, Group C members ran an average of 6.75 miles, and Group D ran an average of 6.50. Since 6.75 is greater than 6.50, Group C ran the most miles.