Question

Cost of 10 oranges and 3 bananas is RS 109 and the cost of 3 oranges and 10 bananas is RS 60 Form linear equations to represent this situation​

Answer 1

Let the

• Cost of oranges be x
• Cost of bananas be y

According to the question;

10x + 3y = 109       → → → [Equation 1]

3x + 10y = 60        → → → [Equation 2]

Let's solve the above 2 equations.

Adding the above 2 equations,

         

                   10x + 3y = 109

           [+]    3x + 10y = 60

                    13x + 13y = 169

Taking 13 as a common factor,

13(x + y) = 169

⇒ x + y = 169 ÷ 13

⇒ x + y = 13          → → → [Equation 3]

Now Subtracting Equation 1 and 2

                   10x + 3y = 109

           [-]    3x + 10y = 60

                   7x - 7y = 49

Taking 7 as a common factor,

7(x - y) = 49

⇒ x - y = 49 ÷ 7

⇒ x - y = 7       → → → [Equation 4]

Adding Equations 3 and 4;

                    x + y = 13

              {+}  x - y = 7

                    2x = 20

⇒ x = 20 ÷ 2

∴ x = 10

Substitute value of x in Equation 3 to find the value of y.

x + y = 13

⇒ 10 + y = 13

⇒ y = 13 - 10

∴ y = 3