Question 971905
1.girls + x ; boys =2x  (2x/4) play soccer (boys) (x/6) girls. 
2/3 of students are boys and half play soccer.  That is 1/3
1/3 of students are girls and 1/6 play soccer.  That is 1/18.  The fraction is 7/18.

2.  The product is positive and lies on the interval (1,infinity).  That occurs when m approaches minus infinity and n approaches -1.  It is 1 when m approaches -1 from the left and n from the right.  
3.The sum of the digits has to be evenly divisible  by 6.  Twenty-four doesn't work, but thirty does work and 555681 works if he multiplies by 563
12. Log 360= log 36 + log 10=1.55+1=2.55
13. green first then (7/11)*(3/10=21/110
yellow first then (5/11)(3/10)=15/110
white first then (5/11)(4/10)=20/110
The probability is 56/110
11.  x = loan 1  1550-x=loan 2
.08x + .06 (1550-x)= 106
.08x +93-.06x=106
.02x=13
x=650   1550-650=900
income is 650@8%=52  other is 900@6%=54

10. in 1 hr.   (1/36) filled  (1/45) filled ;
(x/36) +(x/45) =1
Multiply through by 1620.
45x +36 x=1620=81x
x=20 hours.

Will stop there as time has run out.