Question

In a friut shop the 3kg of apple,2kg of banana,5kg of pine apple is $50and 4 kg of apple ,6 kg of banana and 2kg of pine apple is $40 and 2kg of apple , 6kg of banana ,7kg of pineapple is $70 cost of each item per kg​

Answer 1

Given:

(i) 3kg of apple,2kg of banana,5kg of pine apple is $50

(ii) 4 kg of apple ,6 kg of banana and 2kg of pine apple is $40

(iii) 2kg of apple , 6kg of banana ,7kg of pineapple is $70

To find:

(i) Cost of each, per kg.

Solution:

Let the price of 1 kg of apple,banana, pineapple be $a, $b, $p respectively.

So, 3kg of apple, 2 kg of banana and 5kg of pineapple costs

$(3a+2b+5p)

So, (3a+2b+5p) = 50

⇒ 9a + 6b + 15p = 150

⇒ 6b = 150 - 9a - 15p

Again, 4kg of apple, 6 kg of banana and 2kg of pineapple costs $(4a+6b+2p)

(4a+6b+2p) = 40

Substituting the value of 6b from (1), we get,

⇒ 4a + 150 - 9a - 15p + 2p = 40

⇒ 5a + 13p = 110

⇒ a = 22 - 13p/5 ... (2)

Again, 2kg of apple, 6 kg of banana and 7kg of pineapple costs $(2a+6b+7p)

(2a+6b+7p) = 70

Replacing 6b from (1), here , we get,

2a + 150 - 9a - 15p + 7p = 70

⇒ 8p + 7a = 80

Replacing the value of 'a' from (2),

⇒ 8p + 7(22 - 13p/5) = 80

⇒ 8p + 154 - 91p/5 = 80

⇒ 51p/5 = 74

⇒ p = 74*5/51

= $ 7.25

8p + 7a = 80

⇒ 7a = 80 - 8(7.25)

⇒ 7a = 22

⇒ a = 22/7

= $ 3.14

Again, 6b = 150 - 9a - 15p

= 150 - 9(3.14) - 15(7.25)

= 13

So, b = 13/6

= $ 2.16

So, the prices of apple , banana, pineapple per kg are $3.14, $2.16, $7.25 respectively.