There were girls,boys and women in a park. 2/3 were girls. The ratio of boys to women was 2:1. If there were 12 more girls than boys,how many women were there?

Question

Please help me solve it xD

Answer 1

First I would change the ratios to fractions.

{When considering the ratio of boys to women is 2:1, add the two digits (2 + 1 = 3) and this will be your denominator. Now you have the fractions  2/3 for boys and 1/3 for women.}

Let X be the total number of people in the park.

We already know that 2/3 of the total people (X) are girls. That leaves 1/3·X to be the boys and women. Of that 1/3·X, 2/3 are boys and 1/3 are women (see above how to convert 2:1 to 2/3 and 1/3)

Now apply the fractions together:

Girls are 2/3·X

Boys are 1/3·X·2/3 = 2/9·X

Women are 1/3·X·1/3 = 1/9·X

Notice that the fractions total to 9/9·X or the entire number of people

We know that the number of girls is equal to the number of boys plus 12 so the equation becomes

     2/3·X = 2/9·X +12

To clear the equation of fractions, multiply each term by 9

    18/3·X = 18/9·X + 108

       6X  =  2X  + 108

       4X  = 108

        X  =  27

The number of women is 1/9·X and that would be 1/9(27) = 3.