Ratio Math Problems - Three Term Ratios

Ratio problems: Three-term Ratios

Word problems with three-term ratios involve comparing three quantities in a specific ratio. These problems often require finding unknown quantities based on the given ratio and additional conditions.

Key Steps for Solving Three-Term Ratio Word Problems:

1. Define variables for the quantities in the ratio.
2. Set up an equation based on the total quantity or given conditions.
3. Solve for the common multiplier (x).
4. Find the individual quantities using the multiplier.
5. Check the solution to ensure it makes sense in the context of the problem.

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

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

Example:
A special cereal mixture contains rice, wheat and corn in the ratio of 2:3:5. If a bag of the mixture contains 3 pounds of rice, how much corn does it contain?

Solution:
Step 1: Define variables:
Let the ratio be 2x:3x:5x, where x is a common multiplier.
Step 2:Set up the equation for the corn:
2x = 5
Step 3:Solve for x:
2x = 5
x = 2.5
Answer: The mixture contains 5(2.5) = 7.5 pounds of corn.

Example:
Clothing store A sells T-shirts in only three colors: red, blue and green. The colors are in the ratio of 3 to 4 to 5. If the store has 20 blue T-shirts, how many T-shirts does it have altogether?
Solution:
Step 1: Define variables:
Let the ratio be 3x:4x:5x, where x is a common multiplier.
Step 2: Set up the equation for the blue T-shirt:
4x = 20
Step 3:Solve for x:
4x = 20
x = 5
Step 4:Find the amount for each type of t-shirt:
Red t-shirts = 3(5) = 15
Blue t-shirts = 4(5) = 20
Green t-shirts = 5(5) = 25
Answer: The total number of shirts would be 15 + 25 + 20 = 60.

Printable & Online Ratio & Proportion Worksheets

How to solve Ratio Word Problems with three terms?

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 of 5 to 6 to 10. Find the lengths of the 3 parts.

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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?

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How to solve Two Term and Three Term Ratio Problems?

A Ratio compares two things that have the same units
A Part to Part Ratio compares one thing to another thing
A Part to Total (whole) Ratio compares one thing to the total number

Example:
In a class of 30 students, there are 18 girls and 12 boys.
What is the ratio of boys to girls?
What is the ratio of girls to boys?
What is the ratio of girls to total?

We can have a three term ratio of red to blue to green marbles.

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Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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