Solving Complicated Proportions
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Introduction

    Proportions are used for a variety of goals: determining a 'normal' weight for a baby at a certain age, calculating distances on maps, identifying inventory rates for businesses, ...

    MATHguide has a lessons that explains the mathematical nature of proportions, if you require a refresher on the topic.

      esson: Proportions

    The sections that follow will allow you to understand how to solve complicated proportions that lead to linear and quadratic equations.


    The second type of complicated proportion leads to linear equations. Before progressing, you will need to know how to solve linear equations. Review this lesson, if necessary, before progressing.

      esson: Solving Linear Equations

    Take a look at this example to see how to solve a complicated proportions.

Example: Solve this proportion.

complicated proportion

    We know from our knowledge of proportions (see Proportions) that cross-products must be equal. So, cross-multiply.

complicated proportion cross-multiply

    Cross-multiplying results with these two equal products.

cross-products proportion

    The steps that follow will indicate how the linear equation can be solved for the a-value. Do the distributive property.

solving linear equation from proportion

    Subtract 3a from both sides of the equation.

solving linear equation from proportion

    Add 32 to both sides of the equation.

solving linear equation from proportion

    Divide both sides of the equation by -11.

solving linear equation from proportion

    Rounded to the nearest 10th, the solution is...

solving linear equation from proportion

    This video will inform you as to how to solve this type of complicated proportion.

      ideo: Solving Complicated Proportions

    Try these interactive quizmasters to determine if you have the hang of it.

      uiz: Proportions 2
      uiz: Proportions 2 with Help


    The first type of complicated proportion leads to quadratic equations. Before progressing, you will need to know how to solve quadratic equations. Review this lesson, if necessary, before progressing.

      esson: Solving Quadratic Equations

    Review this example, which will demonstrate how to solve complicated proportions.

Example: Solve this proportion.

complicated proportion leading to quadratic equation

    Like the problem in the previous section (see Solving Complicated Proportions), we can use the cross-products to begin on our journey to solve for the h-value.

cross multiply complicated proportion leading to quadratic equation

    Here are those cross-products.

cross-products complicated proportion leading to quadratic equation

    Multiply the two binomials. A multiplication table is best here (see Multiplying Polynomials for help).

complicated proportion quadratic equation

    Add 40 to both sides of the equation.

complicated proportion quadratic equation

    Now, factor the trinomial (see Factoring Trinomials for help).

complicated proportion quadratic equation factors

    Next, we set the factors equal to zero (see for help).

complicated proportion linear equations

    Last, we solve each equation separately to gain two solutions.

complicated proportion quadratic equation solutions

    Note, be careful to look at the denominators of our original problem. We have to be careful not to get a zero in a denominator because zero denominators are illogical and therefore unacceptable.

    If we substitute h=-4 into the original problem, the denominator is not equal to zero, making it a possible solution. For the same reason, h=2 is another acceptable solution.

    This video will inform you as to how to solve this type of complicated proportion.

      ideo: Solving Complicated Proportions 2

    Try this interactive quizmaster to determine if you digested the lesson above.

      uiz: Proportions 3


    Here are instructional videos that explain all the aspects of solving complicated proportions.

      ideo: Solving Complicated Proportions
      ideo: Solving Complicated Proportions 2


    Try these quizmasters to determine if you understand how to solve complicated proportions.

      uiz: Proportions 2
      uiz: Proportions 2 with Help
      uiz: Proportions 3


    These lessons are related to solving complicated proportions.

      esson: Proportions
      esson: Similar Figures
      esson: Dilations
      esson: Solving Linear Equations
      esson: Factoring Quadratic Polynomials
      esson: Multiplying Binomials
      esson: Solving Quadratic Equations