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:

5 cans of condensed milk and 3 jars of instant coffee cost Rs 27

12 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:

5x + 3y = 27 and

12x + 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 =

○ Step 4:

○ Put x = in equation 1

5x + 3y = 27

5( ) + 3y = 27

3y = 27 -

3y =

y =

y =

Therefore,

x + y = 4 + 0

x + y = 4

- Final Answer:

Correct option is

Option C. 4.

○ Step 2:

○ Now equate coefficient of y

∴ multiply equation 1 by 5 and multiply equation 2 by 3

○ Step 3:

○ Now subtract equation eq. 3 from eq.4

∴ x =

○ Step 4:

○ Put x = in equation 1

y =

Therefore,

x + y = 4 + 0

x + y = 4

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