 # Ratio Math Problems - Three Term Ratios

Ratio problems are word problems that use ratios to relate the different items in the question.

In these lessons, we will learn how to solve ratio word problems that involve three terms.

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### Ratio problems: Three-term Ratios

Example 1:

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: Assign variables :

Let x = amount of corn

Write the items in the ratio as a fraction. Step 2: Solve the equation

2 × x = 3 × 5
2x = 15

Isolate variable x Answer: The mixture contains 7.5 pounds of corn.

Example 2:

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: Assign variables :

Let x = red shirts
y = green shirts

Write the items in the ratios as fractions. Step 2: Solve the equation

Cross Multiply both equations

3 × 20 = x × 4
60 = 4x
x = 15

5 × 20 = y × 4
100 = 4y
y = 25

The total number of shirts would be 15 + 25 + 20 = 60

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. 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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