Question

Solve by using two variables:

The cost of 3 oranges and 12 apples is Rs. 27 and the cost of 5 oranges and 9 apples is Rs.23. Find

the cost of apples per dozen.
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Answer 1

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Let , the cost of one orange and apple be x and y

FIRST CONDITION :

The cost of 3 oranges and 12 apples is Rs. 27 i.e

3x + 12y = 27 ---- (i)

SECOND CONDITION :

The cost of 5 oranges and 9 apples is Rs.23 i.e

5x + 9y = 23 ---- (ii)

Multiply equation (i) by 5 and eq (ii) by 3 , we get

15x + 60y = 135 ---- (iii)

and

15x + 27y = 69 ---- (iv)

Subtract eq (iv) from eq (iii) , we get

15x + 60y - (15x + 27y) = 135 - 69

60y - 27y = 66

33y = 66

y = 66/33

y = 2

Put the value of y = 2 in eq (ii) , we get

5x + 9(2) = 23

5x + 18 = 23

5x = 23 - 18

5x = 5

x = 5/5

x = 1

Hence , the cost of one orange and apple are Rs. 1 and Rs. 2

It implies the cost of apple per dozen is Rs. 2(6) i.e Rs 12

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