Ratio of boys and girls about sports

Question

After completing the boy survey,  it was determined that for every 3 boys who enjoyed soccer,  5 boys enjoyed basketball.  The girl survey had a ratio of the number of girls who enjoyed soccer to the number of girls who enjoyed basketball of 7:1. If the same number boys and girls were surveyed and 90 boys enjoy soccer, how many girls enjoyed each sport?

Answer 1

Let x represent the proportion ration for each category.

 

3X + 5x = 8X

 

So the ratio is 3/8 = 90/ ?   <--- ratio of soccer to the entire group of boys. That is 3/8 of the boys choose soccer

                                                  while 5/8 of the boys choose basketball

 

By cross multiplication, 3 * ? = 8 * 90

 

                                     ? = 8 * 90/3 = 8 * 30 = 240

 

 So there are 240 boys and 240 girls surveyed.

 

90 boys choose soccer while 240-90 = 150 boys choose basketball.

 

7/8 of the girls choose soccer, which is 7/8 x 240 = 7/8 x 240/1 = 7/1 x 30/1 = 210.

1/8 of 240 = 30 as is 240 - 210 = 30. So 30 girls choose basketball.

 

The following table summarizes the answers:

 

                                Soccer             Basketball        Totals

 

Boys                            90                   150                240

 

Girls                          210                     30                240

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Totals                        300                  180           grand total=480

 

The results seem surprising to me, especially girls like soccer. 

Oh well.