Question

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.

Answer 1

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:

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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.