Finite Math Examples

$0.36 = 398 a + b$ , $0.87 = 568 a + b$ , $0.36 = 0.003 a$

Step 1

Solve for $a$ in $0.36 = 0.003 a$ .

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Step 1.1

Rewrite the equation as $0.003 a = 0.36$ .

$0.003 a = 0.36$

$0.36 = 398 a + b$

$0.87 = 568 a + b$

Step 1.2

Divide each term in $0.003 a = 0.36$ by $0.003$ and simplify.

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Step 1.2.1

Divide each term in $0.003 a = 0.36$ by $0.003$ .

$\frac{0.003 a}{0.003} = \frac{0.36}{0.003}$

$0.36 = 398 a + b$

$0.87 = 568 a + b$

Step 1.2.2

Simplify the left side.

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Step 1.2.2.1

Cancel the common factor of $0.003$ .

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Step 1.2.2.1.1

Cancel the common factor.

$\frac{0.003 a}{0.003} = \frac{0.36}{0.003}$

$0.36 = 398 a + b$

$0.87 = 568 a + b$

Step 1.2.2.1.2

Divide $a$ by $1$ .

$a = \frac{0.36}{0.003}$

$0.36 = 398 a + b$

$0.87 = 568 a + b$

$a = \frac{0.36}{0.003}$

$0.36 = 398 a + b$

$0.87 = 568 a + b$

$a = \frac{0.36}{0.003}$

$0.36 = 398 a + b$

$0.87 = 568 a + b$

Step 1.2.3

Simplify the right side.

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Step 1.2.3.1

Divide $0.36$ by $0.003$ .

$a = 120$

$0.36 = 398 a + b$

$0.87 = 568 a + b$

$a = 120$

$0.36 = 398 a + b$

$0.87 = 568 a + b$

$a = 120$

$0.36 = 398 a + b$

$0.87 = 568 a + b$

$a = 120$

$0.36 = 398 a + b$

$0.87 = 568 a + b$

Step 2

Replace all occurrences of $a$ with $120$ in each equation.

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Step 2.1

Replace all occurrences of $a$ in $0.36 = 398 a + b$ with $120$ .

$0.36 = 398 (120) + b$

$a = 120$

$0.87 = 568 a + b$

Step 2.2

Simplify the right side.

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Step 2.2.1

Multiply $398$ by $120$ .

$0.36 = 47760 + b$

$a = 120$

$0.87 = 568 a + b$

$0.36 = 47760 + b$

$a = 120$

$0.87 = 568 a + b$

Step 2.3

Replace all occurrences of $a$ in $0.87 = 568 a + b$ with $120$ .

$0.87 = 568 (120) + b$

$0.36 = 47760 + b$

$a = 120$

Step 2.4

Simplify the right side.

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Step 2.4.1

Multiply $568$ by $120$ .

$0.87 = 68160 + b$

$0.36 = 47760 + b$

$a = 120$

$0.87 = 68160 + b$

$0.36 = 47760 + b$

$a = 120$

$0.87 = 68160 + b$

$0.36 = 47760 + b$

$a = 120$

Step 3

Solve for $b$ in $0.87 = 68160 + b$ .

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Step 3.1

Rewrite the equation as $68160 + b = 0.87$ .

$68160 + b = 0.87$

$0.36 = 47760 + b$

$a = 120$

Step 3.2

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

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Step 3.2.1

Subtract $68160$ from both sides of the equation.

$b = 0.87 - 68160$

$0.36 = 47760 + b$

$a = 120$

Step 3.2.2

Subtract $68160$ from $0.87$ .

$b = - 68159.13$

$0.36 = 47760 + b$

$a = 120$

$b = - 68159.13$

$0.36 = 47760 + b$

$a = 120$

$b = - 68159.13$

$0.36 = 47760 + b$

$a = 120$

Step 4

Replace all occurrences of $b$ with $- 68159.13$ in each equation.

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Step 4.1

Replace all occurrences of $b$ in $0.36 = 47760 + b$ with $- 68159.13$ .

$0.36 = 47760 - 68159.13$

$b = - 68159.13$

$a = 120$

Step 4.2

Simplify $0.36 = 47760 - 68159.13$ .

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Step 4.2.1

Simplify the left side.

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Step 4.2.1.1

Remove parentheses.

$0.36 = 47760 - 68159.13$

$b = - 68159.13$

$a = 120$

$0.36 = 47760 - 68159.13$

$b = - 68159.13$

$a = 120$

Step 4.2.2

Simplify the right side.

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Step 4.2.2.1

Subtract $68159.13$ from $47760$ .

$0.36 = - 20399.13$

$b = - 68159.13$

$a = 120$

$0.36 = - 20399.13$

$b = - 68159.13$

$a = 120$

$0.36 = - 20399.13$

$b = - 68159.13$

$a = 120$

$0.36 = - 20399.13$

$b = - 68159.13$

$a = 120$

Step 5

Since $0.36 = - 20399.13$ is not true, there is no solution.

No solution