Algebra: Ratio Word Problems

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.

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 = 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 = blue marbles for Jane
20 – x = 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.

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 = red shirts
y = green shirts

Write the items in the ratios as fractions.

Step 2: Solve the equation

Cross Multiply both equations

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.

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