Basic Math Examples

$9.5 % = 17 % \cdot (1 - y) + 5 % \cdot (1 - y)$

Step 1

Rewrite the equation as $17 % \cdot (1 - y) + 5 % \cdot (1 - y) = 9.5 %$ .

$17 % \cdot (1 - y) + 5 % \cdot (1 - y) = 9.5 %$

Step 2

Simplify $17 % \cdot (1 - y) + 5 % \cdot (1 - y)$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Convert $17 %$ to a decimal.

$0.17 \cdot (1 - y) + 5 % \cdot (1 - y) = 9.5 %$

Step 2.1.2

Apply the distributive property.

$0.17 \cdot 1 + 0.17 (- y) + 5 % \cdot (1 - y) = 9.5 %$

Step 2.1.3

Multiply $0.17$ by $1$ .

$0.17 + 0.17 (- y) + 5 % \cdot (1 - y) = 9.5 %$

Step 2.1.4

Multiply $- 1$ by $0.17$ .

$0.17 - 0.17 y + 5 % \cdot (1 - y) = 9.5 %$

Step 2.1.5

Convert $5 %$ to a decimal.

$0.17 - 0.17 y + 0.05 \cdot (1 - y) = 9.5 %$

Step 2.1.6

Apply the distributive property.

$0.17 - 0.17 y + 0.05 \cdot 1 + 0.05 (- y) = 9.5 %$

Step 2.1.7

Multiply $0.05$ by $1$ .

$0.17 - 0.17 y + 0.05 + 0.05 (- y) = 9.5 %$

Step 2.1.8

Multiply $- 1$ by $0.05$ .

$0.17 - 0.17 y + 0.05 - 0.05 y = 9.5 %$

Step 2.2

Simplify by adding terms.

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Step 2.2.1

Add $0.17$ and $0.05$ .

$- 0.17 y + 0.22 - 0.05 y = 9.5 %$

Step 2.2.2

Subtract $0.05 y$ from $- 0.17 y$ .

$- 0.22 y + 0.22 = 9.5 %$

Step 3

Convert $9.5 %$ to a decimal.

$- 0.22 y + 0.22 = 0.095$

Step 4

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

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Step 4.1

Subtract $0.22$ from both sides of the equation.

$- 0.22 y = 0.095 - 0.22$

Step 4.2

Subtract $0.22$ from $0.095$ .

$- 0.22 y = - 0.125$

Step 5

Divide each term in $- 0.22 y = - 0.125$ by $- 0.22$ and simplify.

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Step 5.1

Divide each term in $- 0.22 y = - 0.125$ by $- 0.22$ .

$\frac{- 0.22 y}{- 0.22} = \frac{- 0.125}{- 0.22}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $- 0.22$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{- 0.22 y}{- 0.22} = \frac{- 0.125}{- 0.22}$

Step 5.2.1.2

Divide $y$ by $1$ .

$y = \frac{- 0.125}{- 0.22}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Divide $- 0.125$ by $- 0.22$ .

$y = 0.56\overline{81}$