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 area:

- 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.

Related Topics:

More Algebra Word Problems

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= red sweetsWrite the items in the ratio as a fraction.

Step 2: Solve the equation

3 × 120 = 4 ×

x360 = 4

xIsolate 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= blue marbles for Jane

20 –x= red marbles for JaneWe 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

3 ×

x= 2 × (20 –x)

3x= 40 – 2xIsolate variable

xJohn has 12 blue marbles. So, he has 12 – 8 = 4 more blue marbles than Jane.

Answer: John has 4 more blue marbles than Jane.

Example 3:

This is another word problem that involves ratio or proportion.

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?

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 cornWrite the items in the ratio as a fraction.

Step 2: Solve the equation

2 ×

x= 3 × 5

2x= 15Isolate 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= red shirts

y= green shirtsWrite the items in the ratios as fractions.

Step 2: Solve the equation

Cross Multiply both equations

3 × 20 =

x× 4

60 = 4x

x =155 × 20 =

y× 4

100 = 4y

y= 25The total number of shirts would be 15 + 25 + 20 = 60

Answer: There are 60 shirts.

Algebra and Ratios with three terms

Understanding how algebra can help us think about ratios with more than two terms

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