Concept explainers
To Find: All possibilities for N such that the average of N, K, and 35 is 30.
Answer to Problem 10P
Final Answer: All the possible values of N satisfying the given condition are {50,41,32,23,14}
Explanation of Solution
Given Information: It is given that N is a two digit positive integer and on interchanging its digits we get an integer K such that the average of N, K, and 35 is 30.
Formula used: A two digit number is expressed as
Average of 3 numbers a, b, and c (say) =
Calculation: According to the question, we have
N=
K=
The average of N, K, and 35 is 30
So
From (1) and (2), we have
Or
Or
Or
From (3) we have the sum of digits of N is equal to 5
And since N is a two digit positive integer so x and y must be an integer but x cannot be zero.
So the possible values that N can have is 50, 41, 32, 23, 14.
Chapter 3 Solutions
Algebra and Trigonometry: Structure and Method, Book 2
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