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.

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.

50

step-by-step explanation:

24

step-by-step explanation: