SOLUTION: A Travel Company has booked in a group of people on a Rock & Roll Cruise leaving from Sydney. This group is a combination of men, women, boys and girls. There are twice as many wom

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Question 1138829: A Travel Company has booked in a group of people on a Rock & Roll Cruise leaving from Sydney. This group is a combination of men, women, boys and girls. There are twice as many women as girls in this group and ten less men than the number of women. The number of boys is a quarter of the number of men. If there are 180 people booked by the travel company for the cruise, how many men,women,boys and girls are there booked in this group?
Answer by ikleyn(52810) About Me  (Show Source):
You can put this solution on YOUR website!
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Let G be the number of girls; then

the number of women  is 2G;

the number of men    is  (2G - 10),  and

the number of boys   is  %282G-10%29%2F4.



Therefore, the equation for the total number of people in the group is


    2G + G + (2G-10) + %282G-10%29%2F4 = 180.


Multiply both sides by 4; simplify and get  G = 35.


Thus the number of girls is  35.

Then the number of women is  2*35 = 70;

     the number of men  is  2*35 - 10 = 60,  and

     the number of boys is %281%2F4%29%2A60 = 15.


CHECK.  35 + 70 + 60 + 15 = 180.    ! Correct !

Solved.