Basic Math Examples

$4.75 = \frac{21 \cdot (d + 2.25) + 67 \cdot d}{21 + 67}$

Step 1

Rewrite the equation as $\frac{21 \cdot (d + 2.25) + 67 \cdot d}{21 + 67} = 4.75$ .

$\frac{21 \cdot (d + 2.25) + 67 \cdot d}{21 + 67} = 4.75$

Step 2

Multiply both sides by $21 + 67$ .

$\frac{21 \cdot (d + 2.25) + 67 \cdot d}{21 + 67} (21 + 67) = 4.75 (21 + 67)$

Step 3

Simplify.

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Step 3.1

Simplify the left side.

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Step 3.1.1

Simplify $\frac{21 \cdot (d + 2.25) + 67 \cdot d}{21 + 67} (21 + 67)$ .

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Step 3.1.1.1

Cancel the common factor of $21 + 67$ .

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Step 3.1.1.1.1

Cancel the common factor.

$\frac{21 \cdot (d + 2.25) + 67 \cdot d}{21 + 67} (21 + 67) = 4.75 (21 + 67)$

Step 3.1.1.1.2

Rewrite the expression.

$21 \cdot (d + 2.25) + 67 \cdot d = 4.75 (21 + 67)$

Step 3.1.1.2

Simplify each term.

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Step 3.1.1.2.1

Apply the distributive property.

$21 d + 21 \cdot 2.25 + 67 \cdot d = 4.75 (21 + 67)$

Step 3.1.1.2.2

Multiply $21$ by $2.25$ .

$21 d + 47.25 + 67 d = 4.75 (21 + 67)$

Step 3.1.1.3

Add $21 d$ and $67 d$ .

$88 d + 47.25 = 4.75 (21 + 67)$

Step 3.2

Simplify the right side.

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Step 3.2.1

Simplify $4.75 (21 + 67)$ .

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Step 3.2.1.1

Add $21$ and $67$ .

$88 d + 47.25 = 4.75 \cdot 88$

Step 3.2.1.2

Multiply $4.75$ by $88$ .

$88 d + 47.25 = 418$

Step 4

Solve for $d$ .

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Step 4.1

Move all terms not containing $d$ to the right side of the equation.

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Step 4.1.1

Subtract $47.25$ from both sides of the equation.

$88 d = 418 - 47.25$

Step 4.1.2

Subtract $47.25$ from $418$ .

$88 d = 370.75$

Step 4.2

Divide each term in $88 d = 370.75$ by $88$ and simplify.

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Step 4.2.1

Divide each term in $88 d = 370.75$ by $88$ .

$\frac{88 d}{88} = \frac{370.75}{88}$

Step 4.2.2

Simplify the left side.

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Step 4.2.2.1

Cancel the common factor of $88$ .

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Step 4.2.2.1.1

Cancel the common factor.

$\frac{88 d}{88} = \frac{370.75}{88}$

Step 4.2.2.1.2

Divide $d$ by $1$ .

$d = \frac{370.75}{88}$

Step 4.2.3

Simplify the right side.

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Step 4.2.3.1

Divide $370.75$ by $88$ .

$d = 4.21306\overline{81}$