Can someone please help me understand ?

Mathematics
Tutor: None Selected Time limit: 1 Day

The Spache Readability Formula is designed to categorize reading materials for grades 1 through 3. For a passage of text, the variables are S, the number of sentences, W, the number of words, and U, the number of unfamiliar words (words not on a specific list). The formula (as revised) for the grade level is
Grade level = 0.121(w/s)+ 0.082U + 0.659
In this exercise we consider passages having 270 words and using 8 unfamiliar words.
(b) What is the maximum possible number of sentences?

Sep 24th, 2015

Thank you for the opportunity to help you with your question!

First, let G represent Grade level and calculate G: G = 0.121 * (270/S) + 0.082 *8 + 0.659. Simplifying, we get

G = 8.47 / S + 0.656 + 0.659 = 8.47 / S + 1.315, so

G = 8.47 / S + 1.315. Now rewrite the equation so that S is by itself.

First, subtract 1.315 from both sides of the equation, gettinng G - 1.315 = 8.47 /S.  

Then, multiply both sides of the last equation by S, getting S(G - 1.315) = 8.47. 

To get S by itself, divide both sides of the last equation by (G - 1.315) to get S = 8.47 / (G - 1.315) which is valie provide G isn't equal to 1.315 (which it can't be since G can only be 1, 2 or 3).

Now consider the equation S = 8.47 / (G - 1.315). If G were 1, then S would be negative, which makes no sense.

So, G could be 2 or 3. Try both.

S(2) = 8.47/(2-1.315) = 8.47 / (0.685) 

S(3) = 8.47/(3-1.315) = 8.47 / (1.685)

which is bigger, S(2) or S(3)? 

S(2) ~  12.37 ~ 12

S(3) ~ 5.02 ~ 5

So, the maximum number of sentences would be 12 (for grade 2)


Please let me know if you need any clarification. I'm always happy to answer your questions.
Sep 25th, 2015

Studypool's Notebank makes it easy to buy and sell old notes, study guides, reviews, etc.
Click to visit
The Notebank
...
Sep 24th, 2015
...
Sep 24th, 2015
Dec 6th, 2016
check_circle
Mark as Final Answer
check_circle
Unmark as Final Answer
check_circle
Final Answer

Secure Information

Content will be erased after question is completed.

check_circle
Final Answer