Finite Math Examples

$0.1 A + 0.4 B = 35$ , $0.08 + 0.4 B = 7$

Step 1

Solve for $B$ in $0.08 + 0.4 B = 7$ .

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Step 1.1

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

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Step 1.1.1

Subtract $0.08$ from both sides of the equation.

$0.4 B = 7 - 0.08$

$0.1 A + 0.4 B = 35$

Step 1.1.2

Subtract $0.08$ from $7$ .

$0.4 B = 6.92$

$0.1 A + 0.4 B = 35$

$0.4 B = 6.92$

$0.1 A + 0.4 B = 35$

Step 1.2

Divide each term in $0.4 B = 6.92$ by $0.4$ and simplify.

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Step 1.2.1

Divide each term in $0.4 B = 6.92$ by $0.4$ .

$\frac{0.4 B}{0.4} = \frac{6.92}{0.4}$

$0.1 A + 0.4 B = 35$

Step 1.2.2

Simplify the left side.

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Step 1.2.2.1

Cancel the common factor of $0.4$ .

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Step 1.2.2.1.1

Cancel the common factor.

$\frac{0.4 B}{0.4} = \frac{6.92}{0.4}$

$0.1 A + 0.4 B = 35$

Step 1.2.2.1.2

Divide $B$ by $1$ .

$B = \frac{6.92}{0.4}$

$0.1 A + 0.4 B = 35$

$B = \frac{6.92}{0.4}$

$0.1 A + 0.4 B = 35$

$B = \frac{6.92}{0.4}$

$0.1 A + 0.4 B = 35$

Step 1.2.3

Simplify the right side.

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Step 1.2.3.1

Divide $6.92$ by $0.4$ .

$B = 17.3$

$0.1 A + 0.4 B = 35$

$B = 17.3$

$0.1 A + 0.4 B = 35$

$B = 17.3$

$0.1 A + 0.4 B = 35$

$B = 17.3$

$0.1 A + 0.4 B = 35$

Step 2

Replace all occurrences of $B$ with $17.3$ in each equation.

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Step 2.1

Replace all occurrences of $B$ in $0.1 A + 0.4 B = 35$ with $17.3$ .

$0.1 A + 0.4 (17.3) = 35$

$B = 17.3$

Step 2.2

Simplify the left side.

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Step 2.2.1

Multiply $0.4$ by $17.3$ .

$0.1 A + 6.92 = 35$

$B = 17.3$

$0.1 A + 6.92 = 35$

$B = 17.3$

$0.1 A + 6.92 = 35$

$B = 17.3$

Step 3

Solve for $A$ in $0.1 A + 6.92 = 35$ .

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Step 3.1

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

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Step 3.1.1

Subtract $6.92$ from both sides of the equation.

$0.1 A = 35 - 6.92$

$B = 17.3$

Step 3.1.2

Subtract $6.92$ from $35$ .

$0.1 A = 28.08$

$B = 17.3$

$0.1 A = 28.08$

$B = 17.3$

Step 3.2

Divide each term in $0.1 A = 28.08$ by $0.1$ and simplify.

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Step 3.2.1

Divide each term in $0.1 A = 28.08$ by $0.1$ .

$\frac{0.1 A}{0.1} = \frac{28.08}{0.1}$

$B = 17.3$

Step 3.2.2

Simplify the left side.

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Step 3.2.2.1

Cancel the common factor of $0.1$ .

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Step 3.2.2.1.1

Cancel the common factor.

$\frac{0.1 A}{0.1} = \frac{28.08}{0.1}$

$B = 17.3$

Step 3.2.2.1.2

Divide $A$ by $1$ .

$A = \frac{28.08}{0.1}$

$B = 17.3$

$A = \frac{28.08}{0.1}$

$B = 17.3$

$A = \frac{28.08}{0.1}$

$B = 17.3$

Step 3.2.3

Simplify the right side.

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Step 3.2.3.1

Divide $28.08$ by $0.1$ .

$A = 280.8$

$B = 17.3$

$A = 280.8$

$B = 17.3$

$A = 280.8$

$B = 17.3$

$A = 280.8$

$B = 17.3$

Step 4

Solve the system of equations.

$A = 280.8 B = 17.3$

Step 5

List all of the solutions.

$A = 280.8, B = 17.3$