Finite Math Examples

$a + b + c = 800000$ , $9 a + 0.1 b + 1.1 c = 75200$ , $a = 4 c$

Step 1

Replace all occurrences of $a$ with $4 c$ in each equation.

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Step 1.1

Replace all occurrences of $a$ in $a + b + c = 800000$ with $4 c$ .

$(4 c) + b + c = 800000$

$9 a + 0.1 b + 1.1 c = 75200$

$a = 4 c$

Step 1.2

Simplify the left side.

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Step 1.2.1

Add $4 c$ and $c$ .

$b + 5 c = 800000$

$9 a + 0.1 b + 1.1 c = 75200$

$a = 4 c$

$b + 5 c = 800000$

$9 a + 0.1 b + 1.1 c = 75200$

$a = 4 c$

Step 1.3

Replace all occurrences of $a$ in $9 a + 0.1 b + 1.1 c = 75200$ with $4 c$ .

$9 (4 c) + 0.1 b + 1.1 c = 75200$

$b + 5 c = 800000$

$a = 4 c$

Step 1.4

Simplify the left side.

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Step 1.4.1

Simplify $9 (4 c) + 0.1 b + 1.1 c$ .

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Step 1.4.1.1

Multiply $4$ by $9$ .

$36 c + 0.1 b + 1.1 c = 75200$

$b + 5 c = 800000$

$a = 4 c$

Step 1.4.1.2

Add $36 c$ and $1.1 c$ .

$0.1 b + 37.1 c = 75200$

$b + 5 c = 800000$

$a = 4 c$

$0.1 b + 37.1 c = 75200$

$b + 5 c = 800000$

$a = 4 c$

$0.1 b + 37.1 c = 75200$

$b + 5 c = 800000$

$a = 4 c$

$0.1 b + 37.1 c = 75200$

$b + 5 c = 800000$

$a = 4 c$

Step 2

Subtract $5 c$ from both sides of the equation.

$b = 800000 - 5 c$

$0.1 b + 37.1 c = 75200$

$a = 4 c$

Step 3

Replace all occurrences of $b$ with $800000 - 5 c$ in each equation.

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Step 3.1

Replace all occurrences of $b$ in $0.1 b + 37.1 c = 75200$ with $800000 - 5 c$ .

$0.1 (800000 - 5 c) + 37.1 c = 75200$

$b = 800000 - 5 c$

$a = 4 c$

Step 3.2

Simplify the left side.

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Step 3.2.1

Simplify $0.1 (800000 - 5 c) + 37.1 c$ .

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Step 3.2.1.1

Simplify each term.

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Step 3.2.1.1.1

Apply the distributive property.

$0.1 \cdot 800000 + 0.1 (- 5 c) + 37.1 c = 75200$

$b = 800000 - 5 c$

$a = 4 c$

Step 3.2.1.1.2

Multiply $0.1$ by $800000$ .

$80000 + 0.1 (- 5 c) + 37.1 c = 75200$

$b = 800000 - 5 c$

$a = 4 c$

Step 3.2.1.1.3

Multiply $- 5$ by $0.1$ .

$80000 - 0.5 c + 37.1 c = 75200$

$b = 800000 - 5 c$

$a = 4 c$

$80000 - 0.5 c + 37.1 c = 75200$

$b = 800000 - 5 c$

$a = 4 c$

Step 3.2.1.2

Add $- 0.5 c$ and $37.1 c$ .

$80000 + 36.6 c = 75200$

$b = 800000 - 5 c$

$a = 4 c$

$80000 + 36.6 c = 75200$

$b = 800000 - 5 c$

$a = 4 c$

$80000 + 36.6 c = 75200$

$b = 800000 - 5 c$

$a = 4 c$

$80000 + 36.6 c = 75200$

$b = 800000 - 5 c$

$a = 4 c$

Step 4

Solve for $c$ in $80000 + 36.6 c = 75200$ .

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Step 4.1

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

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Step 4.1.1

Subtract $80000$ from both sides of the equation.

$36.6 c = 75200 - 80000$

$b = 800000 - 5 c$

$a = 4 c$

Step 4.1.2

Subtract $80000$ from $75200$ .

$36.6 c = - 4800$

$b = 800000 - 5 c$

$a = 4 c$

$36.6 c = - 4800$

$b = 800000 - 5 c$

$a = 4 c$

Step 4.2

Divide each term in $36.6 c = - 4800$ by $36.6$ and simplify.

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Step 4.2.1

Divide each term in $36.6 c = - 4800$ by $36.6$ .

$\frac{36.6 c}{36.6} = \frac{- 4800}{36.6}$

$b = 800000 - 5 c$

$a = 4 c$

Step 4.2.2

Simplify the left side.

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Step 4.2.2.1

Cancel the common factor of $36.6$ .

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Step 4.2.2.1.1

Cancel the common factor.

$\frac{36.6 c}{36.6} = \frac{- 4800}{36.6}$

$b = 800000 - 5 c$

$a = 4 c$

Step 4.2.2.1.2

Divide $c$ by $1$ .

$c = \frac{- 4800}{36.6}$

$b = 800000 - 5 c$

$a = 4 c$

$c = \frac{- 4800}{36.6}$

$b = 800000 - 5 c$

$a = 4 c$

$c = \frac{- 4800}{36.6}$

$b = 800000 - 5 c$

$a = 4 c$

Step 4.2.3

Simplify the right side.

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Step 4.2.3.1

Divide $- 4800$ by $36.6$ .

$c = - 131.14754098$

$b = 800000 - 5 c$

$a = 4 c$

$c = - 131.14754098$

$b = 800000 - 5 c$

$a = 4 c$

$c = - 131.14754098$

$b = 800000 - 5 c$

$a = 4 c$

$c = - 131.14754098$

$b = 800000 - 5 c$

$a = 4 c$

Step 5

Replace all occurrences of $c$ with $- 131.14754098$ in each equation.

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Step 5.1

Replace all occurrences of $c$ in $b = 800000 - 5 c$ with $- 131.14754098$ .

$b = 800000 - 5 \cdot - 131.14754098$

$c = - 131.14754098$

$a = 4 c$

Step 5.2

Simplify the right side.

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Step 5.2.1

Simplify $800000 - 5 \cdot - 131.14754098$ .

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Step 5.2.1.1

Multiply $- 5$ by $- 131.14754098$ .

$b = 800000 + 655.73770491$

$c = - 131.14754098$

$a = 4 c$

Step 5.2.1.2

Add $800000$ and $655.73770491$ .

$b = 800655.73770491$

$c = - 131.14754098$

$a = 4 c$

$b = 800655.73770491$

$c = - 131.14754098$

$a = 4 c$

$b = 800655.73770491$

$c = - 131.14754098$

$a = 4 c$

Step 5.3

Replace all occurrences of $c$ in $a = 4 c$ with $- 131.14754098$ .

$a = 4 (- 131.14754098)$

$b = 800655.73770491$

$c = - 131.14754098$

Step 5.4

Simplify the right side.

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Step 5.4.1

Multiply $4$ by $- 131.14754098$ .

$a = - 524.59016393$

$b = 800655.73770491$

$c = - 131.14754098$

$a = - 524.59016393$

$b = 800655.73770491$

$c = - 131.14754098$

$a = - 524.59016393$

$b = 800655.73770491$

$c = - 131.14754098$

Step 6

List all of the solutions.

$a = - 524.59016393, b = 800655.73770491, c = - 131.14754098$