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# Ratio Word Problems

Before proceeding to the Ratio Table, let’s define a Ratio.

A ratio is a comparison of two quantities. A proportion is an equality of two ratios.

The ratio can be represented in three different forms, such as:

•         a to b
•         a : b
•         a/b

Here, “a” is the first term or antecedent, and “b” is the second term or consequent.

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Ratio can be expressed in many ways:

Ratio         Fraction       Decimal       Percentage

2 : 5           2/5             0.4               40%

As given above, the ratios a:b and c:d are in proportion if ad = bc

The ratio should exist between the quantities of the same kind

Example : The ratio can be 32 cm : 54 cm and cannot be 32 cm : 54 kg

Multiplying or dividing each term of the ratio by the same number (non-zero) doesn’t affect the ratio.

Example: 4:9 = 8:18 = 12:27

If a/b = c/d then a : b :: c : d

Now, let’s learn Ratios that are used in real life situations with the help of word problems.

One word problem is best represented in the diagram given below: There have been times when we booked them last minute, but the teachers have been extremely well-prepared and the help desk at etutorworld is very prompt.

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Example 1

There are 8 red marbles, 4 blue marbles and 12 green marbles in a bag. Find the ratio of the following in simplified form

1. a) blue to red marbles
2. b) red to green marbles

(iii) blue to total marbles

Solution:

Total marbles in the bag = 8 + 4 + 12 = 24

Ratio of blue to red marbles = 4 : 8 = 1 : 2

Ratio of red to green = 8 : 12 = 2 : 3

Ratio of green to total = 4 : 24 = 1 : 6

Example 2

Gilbert works in a factory and earns \$1600. He saves \$250 per month. Find the ratio of

1. a) his savings to his income
2. b) his income to his expenditure

Solution:

Gilbert’s income = \$1600

Gilbert’s savings : \$250

Gilbert’s expenditure : 1600 – 250 = 1350

1. a) Gilbert’s savings : his income = 250 : 1600 = 5 : 32
2. b) Gilbert’s income : his expenditure  = 1600 : 1350 =  32 : 27

Example 3

In a class test, 28 students out of 77 passed. Find the ratio between the

1. a) passed students to the total number of students
2. b) failed students to the passed students

Solution:

Total number of students = 77

Number of students passed = 28

Number of students failed = 49

1. a) passed : total = 28 : 77 = 4 : 11
2. b) failed : passed = 49 : 28 = 7 : 4

Example 4

If the ratio of boys and girls on the team is 2:5 and there are 21 girls, how many boys are there?

Solution:

Let number of boys be 2y

Number of girls will be 5y

Total number of boys and girls = 2y + 5y = 7y

Number of boys = 2y/7y x 21 = 6

## FAQs

#### What are ratio word problems?

Ratio word problems are mathematical problems that involve describing and solving situations by comparing quantities using ratios. These problems are commonly encountered in real-life scenarios.

#### How do I approach solving ratio word problems?

When solving ratio word problems, it’s essential to understand the context of the problem, set up the appropriate ratio, and use this ratio to find the desired solution, often involving cross-multiplication.

#### What are some common types of ratio word problems?

Common types of ratio word problems include problems related to mixing solutions, sharing items among people, comparing prices, and determining proportions in recipes.

#### How do I interpret the given information in a ratio word problem?

To interpret the information, identify the quantities being compared and determine whether you need to find a missing quantity, determine the ratio, or make comparisons based on the given information.

#### How do I know if I need to simplify the ratio in a word problem?

You should simplify the ratio if the problem specifies the answer in its simplest form or if you want to make comparisons more accessible. Simplifying ratios involves dividing both parts by their greatest common factor. Gloria Mathew writes on math topics for K-12. A trained writer and communicator, she makes math accessible and understandable to students at all levels. Her ability to explain complex math concepts with easy to understand examples helps students master math. LinkedIn

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