Question

1 jackfruit costs Rs. 19.00, 1 coconut costs Rs. 2.00, a banana costs only Rs. 0.50p. You have Rs 100 and you r to buy 100 numbers of these three fruits. In what combination of these three fruits will you buy so as to their total cost and total numbers will be 100????

Answer 1

SOLUTION

GIVEN

1 jackfruit costs Rs. 19.00, 1 coconut costs Rs. 2.00, a banana costs only Rs. 0.50p.

You have Rs 100 and you r to buy 100 numbers of these three fruits.

TO DETERMINE

In what combination of these three fruits will you buy so as to their total cost and total numbers will be 100

EVALUATION

Let x jackfruit , y coconut and z bananas are purchased

By the first condition

$\displaystyle \sf{ \: 19x + 2y + \frac{z}{2} = 100}$

$\displaystyle \sf{ \implies \: 38x + 4y + z = 200 \: \: \: - - - - (1)}$

By the second given condition

x + y + z = 100 - - - - (2)

Equation 1 - Equation 2 gives

37x + 3y = 100 - - - - (3)

Since HCF( 37, 3) = 1

So Equation 3 possesses unique solution

x = 1 gives y = 21

Thus we get from Equation 2

z = 78

Hence 1 jackfruit , 21 coconut and 78 bananas are purchased

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