Finance Problem but its basic math, i just cant see it right now

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The discussion revolves around solving a finance problem related to calculating the weighted average cost of capital (WACC). The correct formula is presented, leading to the conclusion that the weight of debt (wd) is 30%. The participant initially struggled with the calculations and resorted to plugging in answers to find the solution. They later clarified their method, realizing that the sum of weights must equal 100%, which helped them understand the relationship between wd and the weight of equity. The participant seeks to grasp the correct approach to the problem rather than relying on trial and error.
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Homework Statement



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%.



Homework Equations





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. I am just trying to figure out how the correct way was.
 

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