Let the number be x.
40% of the number is = [tex] (x) (\frac{40}{100} ) [/tex]
20% of 40% of the number is = [tex] (x)(\frac{40}{100} )(\frac{20}{100} ) [/tex]
= [tex] (x)(0.4)(0.2) [/tex]
Given 20% of 40% of the number x is 10 greater than half the number x.
Half the number x = [tex] \frac{x}{2} [/tex]
So we can write the equation as ,
[tex] (x)(0.4)(0.2) = \frac{x}{2} +10 [/tex]
[tex] (x)(0.08) = (0.5x)+10 [/tex]
[tex] (0.08x) = (0.5x) +10 [/tex]
Now to find x, we will have to move (0.5x) to the left side by subtracting it from both sides. We will get,
[tex] (0.08x) -(0.5x) = (0.5x) -(0.5x) +10 [/tex]
[tex] (0.08x) - (0.5x) = 10 [/tex]
[tex] (-0.42x) = 10 [/tex]
Now to find x we will move (-0.42) to the right side by dividing it to both sides.
[tex] \frac{(-0.42x)}{(-0.42)} = \frac{10}{(-0.42)} [/tex]
[tex] x = \frac{10}{(-0.42)} [/tex]
[tex] x= -\frac{(10)(100)}{42} [/tex]
[tex] x=- \frac{1000}{42} [/tex]
We will have to simplify 1000 and 42 by dividing the numerator and denominator by a common factor of it. 2 is a common factor of 1000 and 42.
So by dividing 1000 and 42 by 2 we will get,
[tex] x = - \frac{500}{21} [/tex]
We have got the required answer here. Option A is the correct option here.
