Finite Math Examples

Solve by Substitution 30r+20p=17.40 , 20r+12p=11.04 , 10r+50p=x
, ,
Step 1
Rewrite the equation as .
Step 2
Solve for in .
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Step 2.1
Subtract from both sides of the equation.
Step 2.2
Divide each term in by and simplify.
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Step 2.2.1
Divide each term in by .
Step 2.2.2
Simplify the left side.
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Step 2.2.2.1
Cancel the common factor of .
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Step 2.2.2.1.1
Cancel the common factor.
Step 2.2.2.1.2
Divide by .
Step 2.2.3
Simplify the right side.
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Step 2.2.3.1
Simplify each term.
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Step 2.2.3.1.1
Divide by .
Step 2.2.3.1.2
Cancel the common factor of and .
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Step 2.2.3.1.2.1
Factor out of .
Step 2.2.3.1.2.2
Cancel the common factors.
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Step 2.2.3.1.2.2.1
Factor out of .
Step 2.2.3.1.2.2.2
Cancel the common factor.
Step 2.2.3.1.2.2.3
Rewrite the expression.
Step 2.2.3.1.3
Move the negative in front of the fraction.
Step 3
Replace all occurrences of with in each equation.
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Step 3.1
Replace all occurrences of in with .
Step 3.2
Simplify the right side.
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Step 3.2.1
Simplify .
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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.
Step 3.2.1.1.2
Multiply by .
Step 3.2.1.1.3
Multiply .
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Step 3.2.1.1.3.1
Multiply by .
Step 3.2.1.1.3.2
Combine and .
Step 3.2.1.1.3.3
Multiply by .
Step 3.2.1.1.4
Move the negative in front of the fraction.
Step 3.2.1.2
To write as a fraction with a common denominator, multiply by .
Step 3.2.1.3
Simplify terms.
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Step 3.2.1.3.1
Combine and .
Step 3.2.1.3.2
Combine the numerators over the common denominator.
Step 3.2.1.4
Simplify the numerator.
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Step 3.2.1.4.1
Factor out of .
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Step 3.2.1.4.1.1
Factor out of .
Step 3.2.1.4.1.2
Factor out of .
Step 3.2.1.4.1.3
Factor out of .
Step 3.2.1.4.2
Multiply by .
Step 3.2.1.4.3
Add and .
Step 3.2.1.4.4
Multiply by .
Step 3.3
Replace all occurrences of in with .
Step 3.4
Simplify the left side.
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Step 3.4.1
Simplify .
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Step 3.4.1.1
Simplify each term.
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Step 3.4.1.1.1
Apply the distributive property.
Step 3.4.1.1.2
Multiply by .
Step 3.4.1.1.3
Multiply .
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Step 3.4.1.1.3.1
Multiply by .
Step 3.4.1.1.3.2
Combine and .
Step 3.4.1.1.3.3
Multiply by .
Step 3.4.1.1.4
Move the negative in front of the fraction.
Step 3.4.1.2
To write as a fraction with a common denominator, multiply by .
Step 3.4.1.3
Simplify terms.
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Step 3.4.1.3.1
Combine and .
Step 3.4.1.3.2
Combine the numerators over the common denominator.
Step 3.4.1.4
Simplify each term.
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Step 3.4.1.4.1
Simplify the numerator.
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Step 3.4.1.4.1.1
Factor out of .
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Step 3.4.1.4.1.1.1
Factor out of .
Step 3.4.1.4.1.1.2
Factor out of .
Step 3.4.1.4.1.1.3
Factor out of .
Step 3.4.1.4.1.2
Multiply by .
Step 3.4.1.4.1.3
Add and .
Step 3.4.1.4.1.4
Multiply by .
Step 3.4.1.4.2
Move the negative in front of the fraction.
Step 4
Solve for in .
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Step 4.1
Move all terms not containing to the right side of the equation.
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Step 4.1.1
Subtract from both sides of the equation.
Step 4.1.2
Subtract from .
Step 4.2
Multiply both sides of the equation by .
Step 4.3
Simplify both sides of the equation.
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Step 4.3.1
Simplify the left side.
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Step 4.3.1.1
Simplify .
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Step 4.3.1.1.1
Cancel the common factor of .
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Step 4.3.1.1.1.1
Move the leading negative in into the numerator.
Step 4.3.1.1.1.2
Move the leading negative in into the numerator.
Step 4.3.1.1.1.3
Factor out of .
Step 4.3.1.1.1.4
Cancel the common factor.
Step 4.3.1.1.1.5
Rewrite the expression.
Step 4.3.1.1.2
Cancel the common factor of .
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Step 4.3.1.1.2.1
Factor out of .
Step 4.3.1.1.2.2
Cancel the common factor.
Step 4.3.1.1.2.3
Rewrite the expression.
Step 4.3.1.1.3
Multiply.
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Step 4.3.1.1.3.1
Multiply by .
Step 4.3.1.1.3.2
Multiply by .
Step 4.3.2
Simplify the right side.
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Step 4.3.2.1
Simplify .
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Step 4.3.2.1.1
Multiply .
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Step 4.3.2.1.1.1
Multiply by .
Step 4.3.2.1.1.2
Combine and .
Step 4.3.2.1.1.3
Multiply by .
Step 4.3.2.1.2
Divide by .
Step 5
Replace all occurrences of with in each equation.
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Step 5.1
Replace all occurrences of in with .
Step 5.2
Simplify the right side.
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Step 5.2.1
Simplify .
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Step 5.2.1.1
Multiply by .
Step 5.2.1.2
Divide by .
Step 5.2.1.3
Add and .
Step 5.3
Replace all occurrences of in with .
Step 5.4
Simplify the right side.
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Step 5.4.1
Simplify .
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Step 5.4.1.1
Simplify each term.
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Step 5.4.1.1.1
Multiply by .
Step 5.4.1.1.2
Divide by .
Step 5.4.1.1.3
Multiply by .
Step 5.4.1.2
Subtract from .
Step 6
List all of the solutions.