Precalculus Examples

$x y = 1400$ , $\frac{1}{4 p} \cdot (x^{2} y) = 700$

Step 1

Simplify $\frac{1}{4 p} \cdot ({(\frac{1400}{y})}^{2} y)$ .

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Step 1.1

Simplify the expression.

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Step 1.1.1

Apply the product rule to $\frac{1400}{y}$ .

$\frac{1}{4 p} \cdot (\frac{1400^{2}}{y^{2}} \cdot y) = 700$

$x = \frac{1400}{y}$

Step 1.1.2

Raise $1400$ to the power of $2$ .

$\frac{1}{4 p} \cdot (\frac{1960000}{y^{2}} \cdot y) = 700$

$x = \frac{1400}{y}$

$\frac{1}{4 p} \cdot (\frac{1960000}{y^{2}} \cdot y) = 700$

$x = \frac{1400}{y}$

Step 1.2

Cancel the common factor of $y$ .

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Step 1.2.1

Factor $y$ out of $y^{2}$ .

$\frac{1}{4 p} \cdot (\frac{1960000}{y \cdot y} \cdot y) = 700$

$x = \frac{1400}{y}$

Step 1.2.2

Cancel the common factor.

$\frac{1}{4 p} \cdot (\frac{1960000}{y \cdot y} \cdot y) = 700$

$x = \frac{1400}{y}$

Step 1.2.3

Rewrite the expression.

$\frac{1}{4 p} \cdot \frac{1960000}{y} = 700$

$x = \frac{1400}{y}$

$\frac{1}{4 p} \cdot \frac{1960000}{y} = 700$

$x = \frac{1400}{y}$

Step 1.3

Cancel the common factor of $4$ .

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Step 1.3.1

Factor $4$ out of $4 p$ .

$\frac{1}{4 (p)} \cdot \frac{1960000}{y} = 700$

$x = \frac{1400}{y}$

Step 1.3.2

Factor $4$ out of $1960000$ .

$\frac{1}{4 (p)} \cdot \frac{4 (490000)}{y} = 700$

$x = \frac{1400}{y}$

Step 1.3.3

Cancel the common factor.

$\frac{1}{4 p} \cdot \frac{4 \cdot 490000}{y} = 700$

$x = \frac{1400}{y}$

Step 1.3.4

Rewrite the expression.

$\frac{1}{p} \cdot \frac{490000}{y} = 700$

$x = \frac{1400}{y}$

$\frac{1}{p} \cdot \frac{490000}{y} = 700$

$x = \frac{1400}{y}$

Step 1.4

Multiply $\frac{1}{p}$ by $\frac{490000}{y}$ .

$\frac{490000}{p y} = 700$

$x = \frac{1400}{y}$

$\frac{490000}{p y} = 700$

$x = \frac{1400}{y}$

Step 2

Find the LCD of the terms in the equation.

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Step 2.1

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

$p y, 1$

$x = \frac{1400}{y}$

Step 2.2

The LCM of one and any expression is the expression.

$x = \frac{1400}{y}$

Step 3

Multiply each term in $\frac{490000}{p y} = 700$ by $p y$ to eliminate the fractions.

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Step 3.1

Multiply each term in $\frac{490000}{p y} = 700$ by $p y$ .

$\frac{490000}{p y} \cdot (p y) = 700 (p y)$

$x = \frac{1400}{y}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $p y$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{490000}{p y} \cdot (p y) = 700 (p y)$

$x = \frac{1400}{y}$

Step 3.2.1.2

Rewrite the expression.

$490000 = 700 (p y)$

$x = \frac{1400}{y}$

$490000 = 700 (p y)$

$x = \frac{1400}{y}$

$490000 = 700 (p y)$

$x = \frac{1400}{y}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Remove parentheses.

$490000 = 700 p y$

$x = \frac{1400}{y}$

$490000 = 700 p y$

$x = \frac{1400}{y}$

$490000 = 700 p y$

$x = \frac{1400}{y}$

Step 4

Solve the equation.

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Step 4.1

Rewrite the equation as $700 p y = 490000$ .

$700 p y = 490000$

$x = \frac{1400}{y}$

Step 4.2

Divide each term in $700 p y = 490000$ by $700 y$ and simplify.

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Step 4.2.1

Divide each term in $700 p y = 490000$ by $700 y$ .

$\frac{700 p y}{700 y} = \frac{490000}{700 y}$

$x = \frac{1400}{y}$

Step 4.2.2

Simplify the left side.

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Step 4.2.2.1

Cancel the common factor of $700$ .

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Step 4.2.2.1.1

Cancel the common factor.

$\frac{700 p y}{700 y} = \frac{490000}{700 y}$

$x = \frac{1400}{y}$

Step 4.2.2.1.2

Rewrite the expression.

$\frac{p y}{y} = \frac{490000}{700 y}$

$x = \frac{1400}{y}$

$\frac{p y}{y} = \frac{490000}{700 y}$

$x = \frac{1400}{y}$

Step 4.2.2.2

Cancel the common factor of $y$ .

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Step 4.2.2.2.1

Cancel the common factor.

$\frac{p y}{y} = \frac{490000}{700 y}$

$x = \frac{1400}{y}$

Step 4.2.2.2.2

Divide $p$ by $1$ .

$p = \frac{490000}{700 y}$

$x = \frac{1400}{y}$

$p = \frac{490000}{700 y}$

$x = \frac{1400}{y}$

$p = \frac{490000}{700 y}$

$x = \frac{1400}{y}$

Step 4.2.3

Simplify the right side.

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Step 4.2.3.1

Cancel the common factor of $490000$ and $700$ .

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Step 4.2.3.1.1

Factor $700$ out of $490000$ .

$p = \frac{700 \cdot 700}{700 y}$

$x = \frac{1400}{y}$

Step 4.2.3.1.2

Cancel the common factors.

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Step 4.2.3.1.2.1

Factor $700$ out of $700 y$ .

$p = \frac{700 \cdot 700}{700 (y)}$

$x = \frac{1400}{y}$

Step 4.2.3.1.2.2

Cancel the common factor.

$p = \frac{700 \cdot 700}{700 y}$

$x = \frac{1400}{y}$

Step 4.2.3.1.2.3

Rewrite the expression.

$p = \frac{700}{y}$

$x = \frac{1400}{y}$

$p = \frac{700}{y}$

$x = \frac{1400}{y}$

$p = \frac{700}{y}$

$x = \frac{1400}{y}$

$p = \frac{700}{y}$

$x = \frac{1400}{y}$

$p = \frac{700}{y}$

$x = \frac{1400}{y}$

$p = \frac{700}{y}$

$x = \frac{1400}{y}$