GamerGirl15
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please help and draw pic. In a group of ladybugs there were 10% more male ladybugs than female ladybugs.There were 8 more male ladybugs than female ladybugs How many ladybugs were there in all? Solve this problem in two ways: with the aid of a diagram and with equations. Explain both solution methods, and discuss how they are related.

Respuesta :

Answer:

Let the number of female ladybugs be x.  

Since, male ladybugs are greater in number by 8.  

Therefore, number of male ladybugs = Number of female ladybugs + 8 = x + 8  

So, total number of ladybugs in the group  

= Number of male ladybugs + Number of Female Ladybugs  

= x + 8 + x  

= 2x + 8  

Now, Percentage of male ladybugs  

= [ (Number of male ladybugs) / (Total Number of ladybugs) ] * 100  

= 100(x + 8) / (2x + 8)  

= 100(x + 8) / 2(x + 4)  

= 50(x + 8) / (x + 4)  

= [(50x + 400) / (x + 4)] %  

Percentage of female ladybugs  

= [ (Number of female ladybugs) / (Total Number of ladybugs) ] * 100  

= (100 * x) / (2x + 8)  

= 100x / 2(x + 4)  

= [50x / (x + 4)] %  

But percentage of male ladybugs is 10% more than that of female ladybugs.    So, Percentage of male ladybugs - percentage of female ladybugs = 10  

or [(50x + 400) / (x + 4)] - [50x / (x + 4)] = 10  

or (50x + 400 - 50x) / (x + 4) = 10  

or 400 / (x + 4) = 10  

or 400 = 10x + 40 [By Transposing denominator on LHS to RHS]  

or 10x = 400 - 40  

or 10x = 360  

or x = 36  

So, Number of female ladybugs = 36  

Also, Number of male ladybugs = 36 + 8 = 44  

So total Number of ladybugs = 36 + 44 = 80  

Verification:  

-----------------  

Percentage of female ladybugs = (36/80) * 100 = 45%  

Percentage of male ladybugs = (44/80) * 100 = 55%  

Clearly:  

Percentage of male ladybugs - Percentage of female ladybugs  

= 55% - 45%  

= 10 %  

ALSO:  

Number of male ladybugs - Number of female ladybugs  

= 44 - 36  

= 8  

Hence both the conditions are satisfied and our answer is correct.

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