Basic Math Examples

$6220 = \frac{102000}{y - 54}$

Step 1

Rewrite the equation as $\frac{102000}{y - 54} = 6220$ .

$\frac{102000}{y - 54} = 6220$

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.

$y - 54, 1$

Step 2.2

Remove parentheses.

$y - 54, 1$

Step 2.3

The LCM of one and any expression is the expression.

$y - 54$

Step 3

Multiply each term in $\frac{102000}{y - 54} = 6220$ by $y - 54$ to eliminate the fractions.

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Step 3.1

Multiply each term in $\frac{102000}{y - 54} = 6220$ by $y - 54$ .

$\frac{102000}{y - 54} (y - 54) = 6220 (y - 54)$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $y - 54$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{102000}{y - 54} (y - 54) = 6220 (y - 54)$

Step 3.2.1.2

Rewrite the expression.

$102000 = 6220 (y - 54)$

Step 3.3

Simplify the right side.

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Step 3.3.1

Apply the distributive property.

$102000 = 6220 y + 6220 \cdot - 54$

Step 3.3.2

Multiply $6220$ by $- 54$ .

$102000 = 6220 y - 335880$

Step 4

Solve the equation.

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Step 4.1

Rewrite the equation as $6220 y - 335880 = 102000$ .

$6220 y - 335880 = 102000$

Step 4.2

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

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Step 4.2.1

Add $335880$ to both sides of the equation.

$6220 y = 102000 + 335880$

Step 4.2.2

Add $102000$ and $335880$ .

$6220 y = 437880$

Step 4.3

Divide each term in $6220 y = 437880$ by $6220$ and simplify.

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Step 4.3.1

Divide each term in $6220 y = 437880$ by $6220$ .

$\frac{6220 y}{6220} = \frac{437880}{6220}$

Step 4.3.2

Simplify the left side.

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Step 4.3.2.1

Cancel the common factor of $6220$ .

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Step 4.3.2.1.1

Cancel the common factor.

$\frac{6220 y}{6220} = \frac{437880}{6220}$

Step 4.3.2.1.2

Divide $y$ by $1$ .

$y = \frac{437880}{6220}$

Step 4.3.3

Simplify the right side.

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Step 4.3.3.1

Cancel the common factor of $437880$ and $6220$ .

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Step 4.3.3.1.1

Factor $20$ out of $437880$ .

$y = \frac{20 (21894)}{6220}$

Step 4.3.3.1.2

Cancel the common factors.

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Step 4.3.3.1.2.1

Factor $20$ out of $6220$ .

$y = \frac{20 \cdot 21894}{20 \cdot 311}$

Step 4.3.3.1.2.2

Cancel the common factor.

$y = \frac{20 \cdot 21894}{20 \cdot 311}$

Step 4.3.3.1.2.3

Rewrite the expression.

$y = \frac{21894}{311}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$y = \frac{21894}{311}$

Decimal Form:

$y = 70.39871382 \dots$

Mixed Number Form:

$y = 70 \frac{124}{311}$