Questions: Solve. 0.007(6-k)+0.09(k-4)=1 Select the correct choice below and, if necessary, fill in the answer box to complete your choice A. k= (Type an integer or a simplified fraction.) B. The solution is all real numbers. C. There is no solution.

Solve. 0.007(6-k)+0.09(k-4)=1 Select the correct choice below and, if necessary, fill in the answer box to complete your choice A. k= (Type an integer or a simplified fraction.) B. The solution is all real numbers. C. There is no solution.
Transcript text: Solve. \[ 0.007(6-k)+0.09(k-4)=1 \] Select the correct choice below and, if necessary, fill in the answer box to complete your choic A. $\mathrm{k}=$ $\square$ (Type an integer or a simplified fraction.) B. The solution is all real numbers. C. There is no solution.
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Solution

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Solution Steps

Step 1: Distribute the coefficients

First, distribute the coefficients across the parentheses: \[ 0.007(6 - k) + 0.09(k - 4) = 1 \] \[ 0.007 \cdot 6 - 0.007k + 0.09k - 0.09 \cdot 4 = 1 \] \[ 0.042 - 0.007k + 0.09k - 0.36 = 1 \]

Step 2: Combine like terms

Combine the like terms: \[ (0.09k - 0.007k) + (0.042 - 0.36) = 1 \] \[ 0.083k - 0.318 = 1 \]

Step 3: Isolate the variable

Add \(0.318\) to both sides of the equation to isolate the term with \(k\): \[ 0.083k = 1 + 0.318 \] \[ 0.083k = 1.318 \]

Step 4: Solve for \(k\)

Divide both sides by \(0.083\) to solve for \(k\): \[ k = \frac{1.318}{0.083} \] \[ k \approx 15.8795 \]

Final Answer

\[ \boxed{k = \frac{659}{50}} \]

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