Help with manipulating an algebraic equation?

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Fogel

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Apr 23, 2019
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Hello, I have an algebra equation with which I wanted to ask help:

1 - 1100/N = 0.998

The object is to solve for "N", and the exercise even shows the steps and the answer, but I can't think of what rule is used to get to this next step:

N = 1100 / (1-0.988)
(and the answer is) N = 91667

When I try to solve for "N", I try various things, like multiplying both sides by "N" to start off, but I haven't been able to discover "how they get" the "1 - 0.988" in the denominator in that middle step. I am baffled (and embarrassed). Is there something simple I'm forgetting?
 
Hello, and welcome to FMH! :)

If we add [MATH]\frac{1100}{N}-0.988[/MATH] to both sides, we get:

[MATH]1-0.988=\frac{1100}{N}[/MATH]
Then we can invert both sides:

[MATH]\frac{1}{1-0.988}=\frac{N}{1100}[/MATH]
Multiply by 1100 and arrange as:

[MATH]N=\frac{1100}{1-0.988}[/MATH]
 
Another way. As long as C is not zero, the numbers B and C can swap places when you have an equation in the form A/B = C

1 - 1100/N = 0.998

Subtract 1 from each side

-1100/N = -0.002

This equation is now in the form A/B=C, so we can swap B and C.

-1100/-0.002 = N

Simplify, to finish.

?
 
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