Question 1206765
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Hi
40% of the seats in a concert are for children. The number of seats for men and women are 5 to 7 respectively. After renovations the number of seats increased by 20%. The number of children seats are 720.
How many seats for adults after the renovations. 
How many women seats after the renovations 
Thanks

Let original number of seats, be S
Number of seats after renovations: 1.2S
Children's number of seats, before and after renovations: .4S and .4(1.2S) = .48S. The actual number
for this happens to be 720.
Adults' number of seats, before and after renovations: .6S and .6(1.2S) = .72S. Let the number for
this be A.
              We then get the following PROPORTION: {{{matrix(2,3, .48S/(.72S), "=", 720/A, 2/3, "=", 720/A)}}}
                                                        2A = 3(720)------ Cross-multiplying
<font color = red><font size = 4><b>Number of adults' seats, after renovations</font></font></b>, or {{{matrix(1,7, A, "=", 3(720)/2, "=", 3(360), "=", highlight("1,080"))}}} 
<font color = red><font size = 4><b>Number of women's seats, after renovations</font></font></b>: {{{matrix(1,7, (7/(5 + 7))("1,080"), "=", (7/12)("1,080"), "=", 7(90), "=", highlight(630))}}} 

BTW, the other person who responded is partly WRONG!</pre>