Word Problems Representation


 
 
Concept Explanation
 

Word Problems Representation

We have to examine the statement clearly and identify our supposition.

After assuming the variable we write the statement mathematically

Illustration: A cab charges per person Rs 15 for the first Kilometer and Rs 10 for each subsequent kilometer. For a distance of x km formulate an equation for the amount charged as y rs.

Solution: Assuming distance as x km

Assuming Amount as y Rs

For the first kilometer Amount = 15 Rs

The number of remaining Kilometer = x-1

Amount for remaining kilometers Amount = (x-1) X 10

Total Amount = Amount for First Kilometer + Amount for Remaining Kilometer

y= 15+(x-1)X 10

y= 15 + 10x -10

y= 10x+5

Illustration: In  countries like USA and Canada, temperature is measured in Fahrenheit,whereas in countries like India,it is measured in Celsius.Here is a linear equation that converts Fahrenheit to Celsius:

F=left ( frac{9}{5} right )C+32

  • Draw the graph of the linear equation given above,assuming Celsius for x-axis and Fahrenheit for y-axis.
  • If the temperature is 350C ,what is the temperature in Fahrenheit ?

  • If the temperature is 990F,what is the temperature in Celsius ?

  • If the temperature is 00C ,what is the temperature in Fahrenheit and is the temperature is 00F,what is the temperature in Celsius?
  • Is there a temperature which is numerically the same in both Fahrenheit and Celsius ?If yes,find it .
  • Solution: We have F =frac{9}{5}C+32 When C = 0 , F =frac{9}{5}(0)+32 = 32 When C = 15, F =frac{9}{5}(15)+32 =27+ 32=59 When C = -10, F =frac{9}{5}(-10)+32 =;-18+ 32=14

    We have the following table: :

    C 0  -15  - 10
    F 32 5 14

    Plotting the ordered pairs (0, 32), (-15, 5) and (-10,14) on a graph paper. Joining these points, we get a straight line AB.

    2. From the graph, we have 86°F corresponds to 30°C. 3. From the graph, we have 95°F corresponds 35°C. 4. We have, C = 0 From (1), we get F =frac{9}{5}(0)+32 = 32

    Also, F = 0 From (1), we get 0=frac{9}{5}(C)+32

    frac{9}{5}(C)=;-32

    C=frac{- 32 X 5}{9}

    C=frac{- 160}{9}

    C=- 17.8

    5. When F = C (numerically) From (1), we get F = frac{9}{5}F +32

    F - frac{9}{5}F = 32

    frac{5F - 9F}{5} = 32

    frac{- 4F}{5} = 32

    F =frac{32 X 5}{- 4}

    F = - 40

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    Sample Questions
    (More Questions for each concept available in Login)
    Question : 1

    "Zoya and Riya, both have total 16 toys". Which of the following linear equations represents this statement?

    Right Option : C
    View Explanation
    Explanation
    Question : 2

    'The length of a rectangle is 4 cm more than twice its breadth'. if a represents the length and b represents the breadth of rectangle then which of the following equations represents the situation?

    Right Option : D
    View Explanation
    Explanation
    Question : 3

    "Ramesh scored thrice as much as Suresh in a board examination", Which of the following linear equations represents this statement?

    Right Option : B
    View Explanation
    Explanation
     
     


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