SOLUTION: Will you please help me with this problem about creating integer coefficients? The whole problem is: The community service club at north middle school is planning to paint apartm

Question 870141: Will you please help me with this problem about creating integer coefficients?
The whole problem is:
The community service club at north middle school is planning to paint apartments at the local senior citizen center next week. The club need your held to determine how many apartments they should be able to paint in a day. Earlier in the year when only 4/7 of the students worked they painted 9 apartments in one day. Next week all of the students are available
A. Assume that all of the workers contribute equally to the work. If X represents the number of apartments that can be painted by all the students in the club, use a multiplier and your understanding of scaling to represent this situation as an equation.
Please help me I don't even know where to start to answer.
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
about the simplest way you can solve this is to set up a ratio as follows;

4/7 of the student body paints 9 apartments.

the whole student body is equal to 7/7 which is equal to 1.

if you let x equal the number of apartments that the whole student body can paint, then you get the ratio:

1/x = (4/7)/9

cross multiply to get 1 * 9 = (4/7) * x.

divide both sides of this equation by (4/7) and you get:

(1 * 9) / (4/7) = x

simplify to get:

x = 63/4 = 15.75.

this says the whole student body, working at the same rate as 4/7 of the student body did, can paint 15.75 apartments in one day.

to test this out, assume that the student body is equal to 175 student.
4/7 of the student body will therefore be equal to 100 students.

your ratio becomes:

175 / x = 100 / 9

cross multiply to get 175 * 9 = 100 * x

simplify to get 1575 = 100 * x

divide both sides of this equation by 100 to get x = 15.75.

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