Kasie M.

asked • 04/01/16

No idea how to solve this algebra problem!

The school cafeteria got rid of some old tables and bought new ones.  Old tables were 2x6, new tables are 2x8.  
 
there are now 24 new tables in the cafeteria.  If the cafeteria has the same table area as before, how many old tables were removed?
 
**edited to read : please double check what the question is asking.  The one person who replied seemed to misunderstand the original question.  Please see my comment below.

Kasie M.

I would have found it simple if they completely replaced the old tables with new tables.  However, my understanding of this question was that they got rid of SOME of the old tables.  They did not say they got rid of ALL.  So I interpreted the question to mean that they kept a combination of 24 new tables and some of the old tables.  ???????
 
Using the ratio of areas 16:12 per table, i found that there are 24 old and 24 new, with a total area of 672.  This means the original number of old tables was 56, but they are only keeping 24, therefore they have to remove 32 old tables.  I have no real idea what I did...it seems crazy.
Report

04/01/16

1 Expert Answer

By:

Victoria V. answered • 04/01/16

Tutor
5.0 (402)

20+ years teaching Algebra 2 subjects & beyond.

See tutors like this
See tutors like this
Area of an old table was 2 x 6 = 12.
 
Area of a new table is 2 x 8 = 16.
 
Since the area of the cafeteria did not change, the number of old tables (n)  took up an area of 12 * n while the number of new tables (16 *24) takes up the same area.  
 
So A (the area of the cafeteria) was 12n.
With the new tables the Area of the cafeteria is 16 * 24 = 384  
 
Since the area of the cafeteria did not change, the A = 12n = 384.
 
Now we just divide both sides by 12 and get that there used to be  (n = )  32 tables. 
 
 
Upvote • 0 Downvote
More
Report

Still looking for help? Get the right answer, fast.

Ask a question for free

Get a free answer to a quick problem.
Most questions answered within 4 hours.

OR

Find an Online Tutor Now

Choose an expert and meet online. No packages or subscriptions, pay only for the time you need.