Question

the cost of 13 cups and 16 spoons is Rs.296,while the cost of 16 cups and 13 spoons is Rs.284.find the cost of 2 cups and 5 spoons.

Answer 1

the cost of 2 cups and 5spoons is 76

Answer 2

Let cost of one cup=x
Cost of one spoon=y
$13x + 16y = 296 \: \: \: \: \: \: \: \: \: \: \: \: \: \: (i) \\ 16x + 13y = 284 \: \: \: \: \: \: \: \: \: \: \: \: \: \: (ii) \\ (i) \times 16 \: \: \: \: 208x + 256y = 4736 \: \: (iii) \\ (ii) \times 13 \: \: \: 208x + 169y = 3692 \: \: (iv) \\ (iii) - (iv) \\ \: \: \: \: 208x + 256y = 4736 \\ - 208x - 169y = - 3692 \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: 87y = 1044 \\ y = 12$
Substituting Value of 'y' in (ii),
$16x + 156 = 284 \\ 16x = 128 \\ x = 8$
Cost of 5 Spoons and 2 Cups
$= 5x + 2y \\ = 5(12) + 2(8) \\ = 60 + 16 \\ = rs76$