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
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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Answer:
7
Step-by-step explanation:
N/A