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Question

There were 24 boys and 20 girls in a chess club last year. This year the number of boys increased by 25% but the number of girls decreased by 10% Part A: was there an increase or decrease  in overall membership?Explain your reasoning. Part B: Find the overall percent change in membership of the club

Answer 1

Jose,

 

Let  Ny = total number of kids in year y (1, 2).

       By = number of boys in year y.

       Gy = number of girls in year y.

 

Then Ny = By + Gy for y=1 and y=2

        N1 = 44  (B1 = 24 and G1 = 20)

       

Now in year 2, B2 = B1 plus 25% increase = 1.25 B1 = 1.25 (24) = 30

                    , G2 = G1 minus 10% decrease = 0.90 G1 = 0.90 (20) = 18

           And     N2 = B2 + G2 = 30 + 18 = 48.

 

Answers:

 

(a)  N2 = 48 is bigger than N1 at 44, so there was an increase of 4.

(b)  N2/N1 = 48/44 = 1.09  , there was a 9% increase in membership. Also could have computed 4/44 for the increase.

Answer 2

percent change = 100*(difference/original)

 

original boys = 24

new boys = 1.25*24 = 30

 

original girls = 20

new girls = 0.9*20 = 18

 

The chess club gained 6 boys and lost 2 girls for a net increase of 4 members

 

The original chess club membership count was 44. The new membership count is 48. The chess club increased by

 

100*(4/44) = 9%