Maths-
General
Easy

Question

A housewife finds that 5 cans of condensed milk and 3 jars of instant coffee cost Rs 27 while 12 cans of condensed milk and 5 jars of instant coffee cost Rs.49. Find the total cost for 7 cans of condensed milk and 2 jars of instant coffee.

Hint:

  • Hint:
○ Form the equation according to given information..
○ Take variable values as x or any alphabet.
○ Solve the equation to get value of x.
○ The concept used in the question is the concept of solving linear equations.
○ Given equations are linear equations in two variables.
○ Methods of Solving Linear Equations.
  • Graphical Method
  • Elimination Method
  • Substitution Method
  • Cross Multiplication Method
  • Matrix Method
  • Determinants Method
○ In the elimination method, any of the coefficients is first equated and eliminated. After elimination, the equations are solved to obtain the other equation.

The correct answer is: x + y = 4


    • Step by step explanation:
    ○ Given:
    rightwards double arrow5 cans of condensed milk and 3 jars of instant coffee cost Rs 27
    rightwards double arrow12 cans of condensed milk and 5 jars of instant coffee cost Rs.49.
    ○ Step 1:
    ○ Let, cost of can of condensed milk be x and cost of jar of instant coffee be y.
    so,
    According to given information:

    rightwards double arrow5x + 3y = 27 and

    rightwards double arrow12x + 5y = 49

    ○ Step 2:

    5x + 3y = 27

    12x + 5y = 49

    ○    Let,

    5x + 3y = 27 —------ eq.1

    12x + 5y = 49 —---------eq.2
    ○ Step 2:
    ○ Now equate coefficient of y
    ∴ multiply equation 1 by 5 and multiply equation 2 by 3

    [5x + 3y = 27  ] 5

    25x + 15y = 135 —---- eq.3

    [12x + 5y = 49  ] 3

    36x + 15y = 147 —---- eq.4
    ○ Step 3:
    ○ Now subtract equation eq. 3 from eq.4

    36x + 15y = 147

    -  25x - 15y = - 135

    —--------------------

    11x = 12
    ∴ x = 12 over 11
    ○ Step 4:
    ○ Put x = 12 over 11 in equation 1

    5x + 3y = 27

    5( 12 over 11 ) + 3y = 27

    3y = 27 -  60 over 11

    3y = fraction numerator left parenthesis 27 space cross times space 11 right parenthesis space minus space 60 over denominator 11 end fraction

    y = fraction numerator left parenthesis 297 right parenthesis space minus space 60 over denominator 11 space cross times space 3 end fraction
    y = 237 over 33
    Therefore,
    x + y = 4 + 0
    x + y = 4

    • Final Answer:
    Correct option is
    Option C. 4.

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