Question

If 20 percent of 40 percent of a number is 10 greater than half the number, what is the number?

Answer 1

0.2*0.4n = 0.5n + 10

0.08n = 0.5n + 10

-0.42n = 10

n = 10/-0.42

n = -500/21

Answer 2

Let the number be x.

40% of the number is = $(x) (\frac{40}{100} )$

20% of 40% of the number is = $(x)(\frac{40}{100} )(\frac{20}{100} )$

= $(x)(0.4)(0.2)$

Given 20% of 40% of the number x is 10 greater than half the number x.

Half the number x = $\frac{x}{2}$

So we can write the equation as ,

$(x)(0.4)(0.2) = \frac{x}{2} +10$

$(x)(0.08) = (0.5x)+10$

$(0.08x) = (0.5x) +10$

Now to find x, we will have to move (0.5x) to the left side by subtracting it from both sides. We will get,

$(0.08x) -(0.5x) = (0.5x) -(0.5x) +10$

$(0.08x) - (0.5x) = 10$

$(-0.42x) = 10$

Now to find x we will move (-0.42) to the right side by dividing it to both sides.

$\frac{(-0.42x)}{(-0.42)} = \frac{10}{(-0.42)}$

$x = \frac{10}{(-0.42)}$

$x= -\frac{(10)(100)}{42}$

$x=- \frac{1000}{42}$

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,

$x = - \frac{500}{21}$

We have got the required answer here. Option A is the correct option here.