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Question

Please help with this qns. Student has yet to learn algebra.

Jane and her friends calculated the average books they had. If Jane had 10 more books than what she had, the average number of books they had will be 75. If she had 6 fewer books, the average number of books they had will be 73. How many friends did jane have?

Answer

Method 1 :
10 + 6 = 16
75 – 73 = 2
16/2 = 8
8 – 1 = 7

Method 2 :
Scenario 1 : If Jane had 10 more books than what she had,
[(number of friends + 1) x number of books] + 10 ——- 75 x (number of friends + 1)
(number of friends x number of books) + 1 x number of books + 10 ——- 75 x number of friends + 75

Scenario 2 : If Jane had 6 fewer books than what she had,
[(number of friends + 1) x number of books] – 6 ——- 73 x (number of friends + 1)
(number of friends x number of books) + 1 x number of books – 6 ——- 73 x number of friends + 73

16 ——- 2 x number of friends + 2
number of friends ——- (16 – 2)/2 = 7

Ans : 7 friends.

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can you explain method 1 further?

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Method 1 : excess and shortage method
10 + 6 = 16 (excess + shortage)
75 – 73 = 2 (difference)
16/2 = 8
8 – 1 = 7 (less Jane)

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