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Math  /  Algebra

QuestionSolve Bk=N+yy\frac{B}{k}=\frac{N+y}{y} for yy. y=y=

Studdy Solution

STEP 1

What is this asking? We're trying to rearrange this funky equation to get yy all by itself on one side.
It's like a puzzle, and yy is the special piece we want to isolate! Watch out! Don't get tripped up by the fractions!
We'll tackle them strategically.
Also, remember that we can't divide by zero, so keep an eye on those denominators!

STEP 2

1. Multiply both sides to get rid of fractions
2. Group the yy terms
3. Factor out yy
4. Isolate yy

STEP 3

We want to get rid of the kk in the denominator on the left side.
To do that, we multiply **both** sides of the equation by kk.
Remember, what we do to one side, we *must* do to the other to keep things balanced! Bk⋅k=N+yy⋅k \frac{B}{k} \cdot k = \frac{N+y}{y} \cdot k B=k(N+y)y B = \frac{k(N+y)}{y}

STEP 4

Now, let's get that yy out of the denominator on the right side.
We'll multiply **both** sides by yy! B⋅y=k(N+y)y⋅y B \cdot y = \frac{k(N+y)}{y} \cdot y By=k(N+y) By = k(N+y)

STEP 5

Let's distribute that kk on the right side to get rid of the parentheses. By=k⋅N+k⋅y By = k \cdot N + k \cdot y By=kN+ky By = kN + ky

STEP 6

To group all the yy terms together, we'll subtract kyky from **both** sides of the equation. By−ky=kN+ky−ky By - ky = kN + ky - ky By−ky=kN By - ky = kN

STEP 7

Now, we can factor out our star, yy, from the left side! y(B−k)=kN y(B - k) = kN

STEP 8

Finally, to get yy all by itself, we divide **both** sides by (B−k)(B-k). y(B−k)(B−k)=kN(B−k) \frac{y(B - k)}{(B-k)} = \frac{kN}{(B-k)} y=kNB−k y = \frac{kN}{B-k}

STEP 9

y=kNB−k y = \frac{kN}{B-k}

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