Math problem, you any good?

Question

500= (1.96) (4700/sqrt(n)) This is the answer is n = (1.96)^2 (4700)^2 /(500)^2 =339.44

Why is it that, rather than n = (1.96)^2 (4700)^2 - (500)^2
not sure on the algebra why we divide by 500squared rather than subtracting it.

Answer 1

If you look at your expression, the first step is to multiply BOTH sides by sqrt(n). Then you will get:

500sqrt(n) = (1.96)(4700) (because the sqrt(n)/sqrt(n) simplifies to 1)

Now, you must divide both sides by 500 to get:

sqrt(n) = (1.96)(4700)/500 (the 500/500 simplifies to 1)

The key is to see that you need to divide here. Because subtracting: 500sqrt(n) - 500 does not let you simplify.

Answer 2

Ok, let's first get rid of a lot of the distraction. suppose the problem were just

500 = 7/x

To solve for x, you would first multiply both sides by x :

500x = 7

then divide (not subtract) by 500:

x= 7/500


In your problem, 7 is replaced by (1.96)(4700) and x is sqrt(n), so we have

sqrt(n) = (1.96)(4700)/500.

thus n= (everything on the right)^2

Answer 3

The key to solving any equation is to use inverses, in the appropriate order. There is no addition in this equation, so subtraction will not be used to solve it. Ultimately one will get the variable in the numerator isolated on one side of the equation.

500= (1.96) (4700/sqrt(n))

One could divide by 1.96 or multiply by sqrt(n).
It looks easier to multiply by sqrt(n) first to get the variable in the numerator.
500*sqrt(n)= (1.96) (4700/sqrt(n))*sqrt(n)
500*sqrt(n)= (1.96) (4700)*(sqrt(n)/sqrt(n))
The associative and communitive laws allow me to regroup multiplication and division.
500*sqrt(n)= (1.96) (4700)
Now you must divide by 500 since you wish to use the inverse operation of multiplication,
500*sqrt(n)/500= (1.96) (4700)/500
sqrt(n)500/500 = 18.424
sqrt(n)= 18.424
The inverse operation of the sqrt is squaring so:
(sqrt(n))^2= (18.424)^2
n = 339.44