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Two-Term Ratio Word Problems
More Ratio Word Problems
Algebra Lessons
Examples of How to Find Unit Rate or Unit Price. Ryan purchased 3 apples for $1.80. What is the unit price, or the cost of one apple? We want to know the price per apple unit so we set up a ratio with the number of apples in the denominator. The total price goes in the numerator. So the fraction is 1.80/3. Complete the division: 1.80 ÷ 3 =.60. Powered by Create your own unique website with customizable templates. Start studying Math 8 Unit 5: Percent, Ratio, and Rate. Learn vocabulary, terms, and more with flashcards, games, and other study tools. Jobless rates down in 10 states in 2019; employment-population ratios up in 16 states Annual average unemployment rates in 2019 decreased in 10 states, increased in 1, and were little changed in 39 states and the District of Columbia.
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:
- Change the quantities to the same unit if necessary.
- Write the items in the ratio as a fraction.
- Make sure that you have the same items in the numerator and denominator.
Ratio Problems: Two-Term Ratios
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.
How To Solve Word Problems Using Proportions?
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?
- Show Video Lesson
How To Solve Proportion Word Problems?
When solving proportion word problems remember to have like units in the numerator and denominator of each ratio in the proportion.
Examples:
- Biologist tagged 900 rabbits in Bryer Lake National Park. At a later date, they found 6 tagged rabbits in a sample of 2000. Estimate the total number of rabbits in Bryer Lake National Park.
- Mel fills his gas tank up with 6 gallons of premium unleaded gas for a cost of $26.58. How much would it costs to fill an 18 gallon tank?3 If 4 US dollars can be exchanged for 1.75 Euros, how many Euros can be obtained for 144 US dollars?
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
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.
Algebra And Ratios With Three Terms
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.
- Show Video Lesson
Ratio Problems: Two-Term Ratios
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.
How To Solve Word Problems Using Proportions?
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?
- Show Video Lesson
How To Solve Proportion Word Problems?
When solving proportion word problems remember to have like units in the numerator and denominator of each ratio in the proportion.
Examples:
- Biologist tagged 900 rabbits in Bryer Lake National Park. At a later date, they found 6 tagged rabbits in a sample of 2000. Estimate the total number of rabbits in Bryer Lake National Park.
- Mel fills his gas tank up with 6 gallons of premium unleaded gas for a cost of $26.58. How much would it costs to fill an 18 gallon tank?3 If 4 US dollars can be exchanged for 1.75 Euros, how many Euros can be obtained for 144 US dollars?
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
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.
Algebra And Ratios With Three Terms
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.
- Show Video Lesson
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.
Finding Ratio And Unit Rate
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Rates Ratios And Unit Rates
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Math 8 > Unit 5 - Percent, Ratio and Rate
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