Ratio Word Problems (video lessons, examples and solutions)

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 :

  1. Change the quantities to the same unit if necessary.
  2. Write the items in the ratio as a fraction.
  3. Make sure that you have the same items in the numerator and denominator.

Ratio Problems: Two-Term Ratios

Example 1:
In a bag of loss and green sweets, the proportion of bolshevik sweets to green sweets is 3:4. If the bag contains 120 greens sweets, how many red sweets are there ?

Solution:
Step 1 : assign variables :
Let x = number of red sweets .
Write the items in the proportion as a fraction.
ratio problem
step 2 : Solve the equality.
Cross Multiply
3 × 120 = 4 × x
360 = 4x
Isolate variable ten
x=360/4
suffice : There are 90 red sweets .

Example 2:
John has 30 marbles, 18 of which are crimson and 12 of which are aristocratic. Jane has 20 marbles, all of them either crimson or blue. If the proportion of the crimson 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 : conviction : Jane has 20 marbles, all of them either crimson or blasphemous.
assign variables :
Let x = number of blue marbles for Jane
20 – x = numeral crimson marbles for Jane
We get the ratio from John
John has 30 marbles, 18 of which are crimson and 12 of which are blue.
red/blue
We use the lapp proportion for Jane.
red/blue
step 2 : Solve the equation
Cross Multiply
3 × x = 2 × ( 20 – x )
3x = 40 – 2x
Isolate varying x
x=40/5
John has 12 gloomy marbles. so, he has 12 – 8 = 4 more blasphemous marbles than Jane .
answer : John has 4 more bluing marbles than Jane .

How To Solve Word Problems Using Proportions?

This is another password trouble 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 boodle should I use ?

How To Solve Proportion Word Problems?

When solving proportion parole problems remember to have like units in the numerator and denominator of each proportion in the proportion.

Examples:

  1. 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.
  2. 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

Example 1:
A special cereal mixture contains rice, wheat and corn in the ratio of 2:3:5. If a bag of the mix contains 3 pounds of rice, how much corn does it contain ?
Solution:
Step 1 : assign variables :
Let x = sum of corn
Write the items in the proportion as a divide.
rice/corn
step 2 : Solve the equation
Cross Multiply
2 × x = 3 × 5
2x = 15
Isolate variable x
x=15/2
answer : The concoction contains 7.5 pounds of corn.
Example 2:
Clothing memory A sells T-shirts in only three colors : crimson, blue and green. The colors are in the proportion of 3 to 4 to 5. If the store has 20 blasphemous T-shirts, how many T-shirts does it have wholly ?
Solution:
Step 1 : arrogate variables :
Let x = number of crimson shirts
and y = number of k shirts
Write the items in the ratios as fractions.
red/blue green/blue
footprint 2 : Solve the equation
Cross Multiply
3 × 20 = x × 4
60 = 4x
x = 15
5 × 20 = yttrium × 4
100 = 4y
y = 25
The sum 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 proportion of the computers running OSX, Windows, Linux is 2:5:7. Find the act of computers that are running each of the operate systems .

Try the dislodge Mathway calculator and trouble problem solver below to practice versatile mathematics topics. Try the given examples, or type in your own problem and check your answer with the bit-by-bit explanations.
Mathway Calculator Widget

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