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## Algebra: Ratio Word Problems

Related Pages Two-Term Ratio Word Problems More Ratio Word Problems Algebra Lessons

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

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.

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.

## How To Solve Proportion Word Problems?

- 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

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.

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

## Algebra And Ratios With Three Terms

Let’s study how algebra can help us think about ratios with more than two terms.

## Word Problems: Ratios

Write the ratio as a 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 .)

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

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

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

In simplest form, this ratio is 5 : 3 .

Some ratio word problems require you to solve a proportion.

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 .

So, you need to use 9 cups of sugar.

You can think of this in terms of equivalent fractions :

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## Primary Grade Challenge Math by Edward Zaccaro

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## Unit 1: Lesson 4

## Part to whole ratio word problem using tables

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## Video transcript

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.

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

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

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

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.

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

Hence, the larger part is 84, we get

Therefore, the quantity is 144.

- Basic Concept of Ratios
- Important Properties of Ratios
- Ratio in Lowest Term
- Types of Ratios
- Comparing Ratios
- Arranging Ratios
- Dividing into a Given Ratio
- Divide a Number into Three Parts in a Given Ratio
- Dividing a Quantity into Three Parts in a Given Ratio
- Problems on Ratio
- Worksheet on Ratio in Lowest Term
- Worksheet on Types of Ratios
- Worksheet on Comparison on Ratios
- Worksheet on Ratio of Two or More Quantities
- Worksheet on Dividing a Quantity in a Given Ratio
- Definition of Continued Proportion
- Mean and Third Proportional
- Word Problems on Proportion
- Worksheet on Proportion and Continued Proportion
- Worksheet on Mean Proportional
- Properties of Ratio and Proportion
- 10th Grade Math

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## Ratio word problems

## Interesting ratio word problems

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

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

## Hard ratio word problems

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

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Word Problems on Ratio · 1. John weights 65.7 kg. If he reduces his weight in the ratio 5 : 4, find his reduced weight. · 2. Robin leaves $ 1245500 behind. · 3.

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Example #1: · 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