Question

5 kg apples and 9kg grapes together cost Rs 57 and 9kg of apples and 5kg of grapes together cost Rs 69. Represent this situation algebraically and graphically with solution

Answer 1

let apples is x and grapes is y
so,in first condition
5x+9y=57
and in second situation
9x+5y=69
now
5x+9y=57----(x9)
9x+5y=69---(x5)
we will get
45x+81y=513----(1)
45x+25y=345---(2) (subtracting eq 2 from eq 1)
we will get
56y=168
y=168/56
y=3
now putting value of y in equation (1)
5x+9*3=57
5x+27=57
5x=57-27=30
X=30/5= 6
now checking both in equation (1)
5x+9y=57
5*6+9*3=57
30+27=57

Answer 2

Let 1kg apples cost Rs x

Let 1kg grapes cost Rs y

By the problem:

5 kg apples and 9kg grapes together cost Rs 57

this can be mathematically written as-

5x+9y=57  -----eq 1

9 kg of apples and 5 kg of grapes together cost Rs 69.

this can be mathematically written as-

9x+5y=69  -----eq 2

Subtracting eq 1 from 2 we get:

         9x+5y=69

   -     5x+9y=57

  -------------------------------------------------

          4x-4y=12

        =>4(x-y)=12

       =>  x-y=3----eq 3

Multiplying eq 3 with 5 and adding it with eq 2

       9x+5y=69

        5x-5y=15

------------------------

       14x=84

    => x=12

From eq 3 we get x-y=3 =>12-y=3=>y=9

ANS:x=12;y=9

Hope this helps : )