Finance Problem but its basic math, i just cant see it right now (1 Viewer)

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1. The problem statement, all variables and given/known data

A. 53%
B. 40%
C. 30%
D. 70%
E. 36%

Solution: WACC = wd kd (1 - T) + wsks ; 13.00% = wd (9% (1 - 0.35)) + (1 - wd) ($2(1.075)/$25.00 + 7.5%) ; Solve for wd = 30%.



2. Relevant equations



3. The attempt at a solution

ok, i got this one right but i did it by plugging in the answer becus i cld not figure it out. The formula for the answer how they do it is above but simplified i get this: .13=wd(.0585)+(1-wd)(.161)

wd comes out to be 30 percent.

i must be missing something because i can not figure it out
 
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ok sweet i think i got it..

this is what i did.

13=5.85wd+16.1-16.1wd

-3.1=-10.25wd

wd=0.302439024

Since both must equal 100 in this problem. that is why they do 1-wd. What i originally did on the quiz was i just plugged in the answers wd and solved and then w/e was left must equal to 100. so using the 30 i got the common equity to be 70 percent when i plugged it in and BAM problem solved. im just trying to figure out how the correct way was.
 

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