Ratio Word Problems


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Examples, videos, worksheets, solutions, and activities to help Algebra and Grade 9 students learn how to solve ratio word problems using algebra and proportions. The examples include two-term and three-term ratios.




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Ratio problems using Algebra

Solving ratio word problems using algebra involves setting up equations based on the given ratios and solving for the unknown quantities.

Step-by-Step Guide:

  1. Understand the Problem:
    Read the problem carefully and identify the given ratios and the unknown quantities.
  2. Define Variables:
    Assign variables to the unknown quantities.
  3. Set Up a Proportion:
    Write the given ratios as a proportion or express the quantities in terms of the variables.
  4. Form an Equation:
    Use the given conditions to form an equation involving the variables.
  5. Solve the Equation:
    Use algebraic methods (e.g., cross-multiplication, multiplier) to solve for the unknown variables.
  6. Check the Solution:
    Verify that the solution makes sense in the context of the problem.

The following diagram gives the steps to solve a three-term ratio word problem using the multiplier method. Scroll down the page for examples and step-by-step solutions.

Three Term Ratio Word Problems

Ratio Word Problems
Ratio Problems
Two-Term Ratios
Three-Term Ratios
Ratio Word Problems

How to Solve Ratio Word Problems using algebra?
This video shows the trick of multiplying each term in the ratio by x to help set up an equation. This problem contains a ratio with 3 parts.
Example:
At Patwyn’s Pet Store, the ratio of dogs to cats to elephants is 3:5:7. If there are 135 of these animals in total, how many elephants are at Patwyn’s store?

Ratio Word Problems
Students learn that the ratio of one number to another is the result of the first number divided by the second number.
Example:
A piece of string that is 63 inches long is cut into 3 parts such that the lengths of the parts of the string are in the ratio 5 to 6 to 10. Find the lengths of the 3 parts.




How to solve ratio word problems using proportions and algebra?
This video focuses on solving a ratio word problem with two methods. In the first method, the concept of proportions is used to solve the ratio word problem. In the second method, you will see how to combine ratios and algebra to solve a ratio word problem.
Example:
At Euclid High School, the ratio of male students to females students is 5:7. If there are 300 students in total, how many male students are there at Euclid High School?

Ratio Problem (with triangle perimeter) - Geometry
This video focuses on a ratio problem involving the perimeter of a triangle. It uses the method of solving algebraic equations.
Example:
The measure of the sides of a triangle are in the ratio of 4:5:6. Find the measure of each side if the perimeter of the triangles is 105 inches.

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