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Two-Term Ratio Word Problems
More Ratio Word Problems
Algebra Lessons
In these lessons, we will learn how to solve ratio word problems that have two-term ratios or three-term ratios.
Ratio problems are word problems that use ratios to relate the different items in the question.
The main things to be aware about for ratio problems are:
Printable
Introduction to Ratios
Ratio Word Problems using Tape diagrams
Ratio Problems given One of Quantities
Ratio Problems given Total
Ratio Problems given Difference
Ratio Problems with Change of Ratio
Online
Ratio of Quantities
Ratio Word Problems I
Ratio Word Problems II
Ratio Word Problems III
Ratio Word Problems IV
Ratio with Algebra
Example 1:
In a bag of red and green sweets, the ratio of red sweets to green sweets is 3:4. If the bag contains
120 green sweets, how many red sweets are there?
Solution:
Step 1: Assign variables:
Let x = number of red sweets.
Write the items in the ratio as a fraction.
Step 2: Solve the equation.
Cross Multiply
3 × 120 = 4 × x
360 = 4x
Isolate variable x
Answer: There are 90 red sweets.
Example 2:
John has 30 marbles, 18 of which are red and 12 of which are blue. Jane has 20 marbles, all of them
either red or blue. If the ratio of the red marbles to the blue marbles is the same for both John and
Jane, then John has how many more blue marbles than Jane?
Solution:
Step 1: Sentence: Jane has 20 marbles, all of them either red or
blue.
Assign variables:
Let x = number of blue marbles for Jane
20 – x = number red marbles for Jane
We get the ratio from John
John has 30 marbles, 18 of which are red and 12 of which are blue.
We use the same ratio for Jane.
Step 2: Solve the equation
Cross Multiply
3 × x = 2 × (20 – x)
3x = 40 – 2x
Isolate variable x
John has 12 blue marbles. So, he has 12 – 8 = 4 more blue marbles than Jane.
Answer: John has 4 more blue marbles than Jane.
This is another word problem that involves ratio or proportion.
Example:
A recipe uses 5 cups of flour for every 2 cups of sugar. If I want to make a recipe using 8 cups of
flour. How much sugar should I use?
When solving proportion word problems remember to have like units in the numerator and denominator of each ratio in the proportion.
Examples:
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
Cross Multiply
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 = number of red shirts
and y = number of green shirts
Write the items in the ratios as fractions.
Step 2: Solve the equation
Cross Multiply
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
Answer: There are 60 shirts.
Let’s study how algebra can help us think about ratios with more than two terms.
Example:
There are a total of 42 computers. Each computer runs one of three operating systems: OSX, Windows,
Linux. The ratio of the computers running OSX, Windows, Linux is 2:5:7. Find the number of computers
that are running each of the operating systems.
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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