how to solve ratio word problems 8th grade

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Algebra: Ratio Word Problems

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:

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.

Step 2: Solve the equation. Cross Multiply 3 × 120 = 4 × x 360 = 4 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

Step 2: Solve the equation

Cross Multiply 3 × x = 2 × (20 – x ) 3 x = 40 – 2 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?

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.

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

Step 2: Solve the equation Cross Multiply 2 × x = 3 × 5 2 x = 15

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

Step 2: Solve the equation Cross Multiply 3 × 20 = x × 4 60 = 4 x x = 15

5 × 20 = y × 4 100 = 4 y 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.

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Word Problems: Ratios

A ratio is a comparison of two numbers. It can be written with a colon ( 1 : 5 ) , or using the word "to" ( 1 to 5 ) , or as a fraction: 1 5

A backyard pond has 12 sunfish and 30 rainbow shiners. Write the ratio of sunfish to rainbow shiners in simplest form .

Write the ratio as a fraction.

Now reduce the fraction .

So the ratio of sunfish to rainbow shiners is 2 : 5 .

(Note that the ratio of rainbow shiners to sunfish is the reciprocal : 5 2 or 5 : 2 .)

Read word problems carefully to check whether the ratio you're being asked for is a fraction of the total or the ratio of one part to another part .

Ms. Ekpebe's class has 32 students, of which 20 are girls. Write the ratio of girls to boys.

Careful! Don't write 20 32 ... that's the fraction of the total number of students that are girls. We want the ratio of girls to boys.

Subtract 20 from 32 to find the number of boys in the class.

32 − 20 = 12

There are 12 boys in the class. So, ratio of girls to boys is 20 : 12 .

You can reduce this ratio, the same way you reduce a fraction. Both numbers have a common fact of 4 , so divide both by 4 .

In simplest form, this ratio is 5 : 3 .

Some ratio word problems require you to solve a proportion.

A recipe calls for butter and sugar in the ratio 2 : 3 . If you're using 6 cups of butter, how many cups of sugar should you use?

The ratio 2 : 3 means that for every 2 cups of butter, you should use 3 cups of sugar.

Here you're using 6 cups of butter, or 3 times as much.

So you need to multiply the amount of sugar by 3 .

3 × 3 = 9

So, you need to use 9 cups of sugar.

You can think of this in terms of equivalent fractions :

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A good book on problem solving with very varied word problems and strategies on how to solve problems. Includes chapters on: Sequences, Problem-solving, Money, Percents, Algebraic Thinking, Negative Numbers, Logic, Ratios, Probability, Measurements, Fractions, Division. Each chapter’s questions are broken down into four levels: easy, somewhat challenging, challenging, and very challenging.

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Unit 1: Lesson 4

Part to whole ratio word problem using tables

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Video transcript

Word Problems on Ratio

We will learn how to divide a quantity in a given ratio and its application in the word problems on ratio.

1. John weights 65.7 kg. If he reduces his weight in the ratio 5 : 4, find his reduced weight.

Let the previous weight be 5x.

x = $\frac{65.7}{5}$

Therefore, the reduce weight = 4 × 13.14 = 52.56 kg.

2. Robin leaves $ 1245500 behind. According to his wish, the money is to be divided between his son and daughter in the ratio 3 : 2. Find the sum received by his son.

We know if a quantity x is divided in the ratio a : b then the two parts are $\frac{ax}{a + b}$ and $\frac{bx}{a + b}$.

Therefore, the sum received by his son = $\frac{3}{3 + 2}$ × $ 1245500

= $\frac{3}{5}$ × $ 1245500

= 3 × $ 249100

= $ 747300

3. Two numbers are in the ratio 3 : 2. If 2 is added to the first and 6 is added to the second number, they are in the ratio 4 : 5. Find the numbers.

Let the numbers be 3x and 2x.

According to the problem,

$\frac{3x + 2}{2x + 6}$ = $\frac{4}{5}$

Therefore, the original numbers are: 3x = 3 × 2 = 6 and 2x = 2 × 2 = 4.

Thus, the numbers are 6 and 4.

4. If a quantity is divided in the ratio 5 : 7, the larger part is 84. Find the quantity.

Let the quantity be x.

Then the two parts will be $\frac{5x}{5 + 7}$ and $\frac{7x}{5 + 7}$.

Hence, the larger part is 84, we get

$\frac{7x}{5 + 7}$ = 84

⟹ $\frac{7x}{12}$ = 84

⟹ 7x = 84 × 12

⟹ 7x = 1008

⟹ x = $\frac{1008}{7}$

Therefore, the quantity is 144.

● Ratio and proportion

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Ratio word problems

This lesson will show you how to solve four easy ratio word problems and three challenging ratio word problems that require more thinking.

Interesting ratio word problems

Example #1:

In a small business, 40 of the employees are men and 30 of the employees are women. What is ratio of women to men?

Solution: The ratio of women to men is 30 to 40, 30:40, or 30/40

Example #2: The length of a rectangular garden is 20 feet and the width is 15 feet. What is ratio of length to width?

The ratio of length to width is 20 to 15, 20:15 or 20/15

Example #3: A hybrid car can go 400 miles on 8 gallons of gas. How far can the car take you with 1 gallon of gas?

Although the problem does not say to find the ratio, it is a ratio word problem. What you need to do is to first write the ratio of number of miles the car can travel to the number of gallons of gas the car has. Then, write the ratio in simplest form. The ratio is 400/8 and in simplest form it is 50/1 after dividing both numerator and denominator by 8. So you can go 50 miles on 1 gallon of gas.

Hard ratio word problems

Example #4: Suppose the width of a soccer field 60 meters and the length is 100 meters. What is the ratio in simplest form of the length to the area of the field?

The area of the field is 60 × 100 = 6000 The ratio of the length to the area is 100 to 6000, 100:6000 or 100/6000

100/6000 = 1/60 The ratio of the length to the area in simplest form is 1/60

Example #5: A geometry test has 30 questions. 6 of the 30 questions are based on chapter 5. What is the ratio of questions from chapter 5 to the other questions on the test?

There are a total of 30 - 6 or 24 other questions on the geometry test. The ratio of questions from chapter 5 to other questions on the test is 6:24 or 6/24

Suppose a math class starts at the beginning of the school year with 12 boys and 8 girls. However, after school resumes in January, 6 new boys and 4 new girls came to the class. Is the ratio of boys to total number of students in the class still the same?

Ratio of boys to total number of students at the beginning of the school year is 12/8 or 3/2 in simplest form.

Ratio of boys to total number of students after school resumes in January is (12 + 6)/(8 + 4) = 18/12 or 3/2 in simplest form. Therefore, the ratio is still the same.

Proportion word problems

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