Math, asked by zfaisal670, 3 months ago

Sam writes on a white board the positive integers from 1 to 6 inclusive, once each. She then writes p additional fives and q sevens on the board. The mean of all the numbers on the board is then 5.3.
What is the smallest possible value of q?

Answers

Answered by amitnrw
17

Given :   Sam writes on a white board the positive integers from 1 to 6 inclusive, once each.

Then p times 5 and q times 7

Mean = 5.3

To Find :  Smallest possible value of q  

Solution:

1 to 6

p times 5

q times 7

Total Terms = 6 + p + q

Sum = 1 + 2 + 3 + 4 + 5 + 6 + 5p  + 7q  

=  15 + 5p + 7q

Mean = 5.3

(15 + 5p + 7q)/( 6 + p + q)  = 5.3

=> 15 + 5p + 7q  = 31.8 + 5.3p + 5.3q

=>  1.7q = 0.3p  + 16.8

=> 17q = 3p  + 168

=> 15q  + 2q = 3p + 3(56)

=> 2q = 3(p + 56 - 5q)

q  = 3k

=> 17 * 3k     > 168

=> 51k > 168

=> k > 3

=> k = 4

q = 3k = 3(4)  = 12

Minimum possible value of q  = 12

Value of p = 12 ( also )

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Answered by 18gudka
6

Answer:

7

Step-by-step explanation:

N/A

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