Solve for k (714.0*1/760)(0.399)=(0.4270/k)(0.0821)(300.1)

$(714 \times \frac{1}{760}) (0.399) = (\frac{0.427}{k}) (0.0821) (300.1)$

Step 1

Rewrite the equation as $\frac{0.427}{k} \cdot 0.0821 \cdot 300.1 = 714 \cdot \frac{1}{760} \cdot 0.399$ .

$\frac{0.427}{k} \cdot 0.0821 \cdot 300.1 = 714 \cdot \frac{1}{760} \cdot 0.399$

Step 2

Simplify $\frac{0.427}{k} \cdot 0.0821 \cdot 300.1$ .

Multiply $\frac{0.427}{k} \cdot 0.0821$ .

Combine $\frac{0.427}{k}$ and $0.0821$ .

$\frac{0.427 \cdot 0.0821}{k} \cdot 300.1 = 714 \cdot \frac{1}{760} \cdot 0.399$

Multiply $0.427$ by $0.0821$ .

$\frac{0.0350567}{k} \cdot 300.1 = 714 \cdot \frac{1}{760} \cdot 0.399$

Multiply $\frac{0.0350567}{k} \cdot 300.1$ .

Combine $\frac{0.0350567}{k}$ and $300.1$ .

$\frac{0.0350567 \cdot 300.1}{k} = 714 \cdot \frac{1}{760} \cdot 0.399$

Multiply $0.0350567$ by $300.1$ .

$\frac{10.52051567}{k} = 714 \cdot \frac{1}{760} \cdot 0.399$

Step 3

Simplify $714 \cdot \frac{1}{760} \cdot 0.399$ .

Cancel the common factor of $2$ .

Factor $2$ out of $714$ .

$\frac{10.52051567}{k} = 2 (357) \cdot \frac{1}{760} \cdot 0.399$

Factor $2$ out of $760$ .

$\frac{10.52051567}{k} = 2 \cdot 357 \cdot \frac{1}{2 \cdot 380} \cdot 0.399$

Cancel the common factor.

$\frac{10.52051567}{k} = 2 \cdot 357 \cdot \frac{1}{2 \cdot 380} \cdot 0.399$

Rewrite the expression.

$\frac{10.52051567}{k} = 357 \cdot \frac{1}{380} \cdot 0.399$

Combine $357$ and $\frac{1}{380}$ .

$\frac{10.52051567}{k} = \frac{357}{380} \cdot 0.399$

Cancel the common factor of $357$ and $380$ .

Rewrite $357$ as $1 (357)$ .

$\frac{10.52051567}{k} = \frac{1 (357)}{380} \cdot 0.399$

Cancel the common factors.

Rewrite $380$ as $1 (380)$ .

$\frac{10.52051567}{k} = \frac{1 \cdot 357}{1 \cdot 380} \cdot 0.399$

Cancel the common factor.

$\frac{10.52051567}{k} = \frac{1 \cdot 357}{1 \cdot 380} \cdot 0.399$

Rewrite the expression.

$\frac{10.52051567}{k} = \frac{357}{380} \cdot 0.399$

Multiply $\frac{357}{380} \cdot 0.399$ .

Combine $\frac{357}{380}$ and $0.399$ .

$\frac{10.52051567}{k} = \frac{357 \cdot 0.399}{380}$

Multiply $357$ by $0.399$ .

$\frac{10.52051567}{k} = \frac{142.443}{380}$

Divide $142.443$ by $380$ .

$\frac{10.52051567}{k} = 0.37485$

Step 4

Find the LCD of the terms in the equation.

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

$k, 1$

The LCM of one and any expression is the expression.

$k$

Step 5

Multiply each term in $\frac{10.52051567}{k} = 0.37485$ by $k$ to eliminate the fractions.

Multiply each term in $\frac{10.52051567}{k} = 0.37485$ by $k$ .

$\frac{10.52051567}{k} k = 0.37485 k$

Simplify the left side.

Cancel the common factor of $k$ .

Cancel the common factor.

$\frac{10.52051567}{k} k = 0.37485 k$

Rewrite the expression.

$10.52051567 = 0.37485 k$

Step 6

Solve the equation.

Rewrite the equation as $0.37485 k = 10.52051567$ .

$0.37485 k = 10.52051567$

Divide each term in $0.37485 k = 10.52051567$ by $0.37485$ and simplify.

Divide each term in $0.37485 k = 10.52051567$ by $0.37485$ .

$\frac{0.37485 k}{0.37485} = \frac{10.52051567}{0.37485}$

Simplify the left side.

Cancel the common factor of $0.37485$ .

Cancel the common factor.

$\frac{0.37485 k}{0.37485} = \frac{10.52051567}{0.37485}$

Divide $k$ by $1$ .

$k = \frac{10.52051567}{0.37485}$

Simplify the right side.

Divide $10.52051567$ by $0.37485$ .

$k = 28.06593482$

Solve for k (714.0*1/760)(0.399)=(0.4270/k)(0.0821)(300.1)

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