Concept explainers
Find the sets of all four consecutive odd positive integers with a sum less than 42.
Answer to Problem 58SR
The set of 3 positive odd numbers are (1,3,5,7) , (3,6,7,9,) , (5,7,9,11) , (7,9,11,13)
Explanation of Solution
Given: Find the sets of all four consecutive odd positive integers with a sum less than 42
Concept Used:
Difference of consecutive even integers is 2.
Condition: Sum of all four consecutive odd positive integers less than 42.
Let the least positive odd number be x, the other three are:
Their sum:
Equation:
Calculation:
Equation:
Solve for x, the least number of the set.
So, the least positive odd number be no more than 7.5.
All possible set of four odd numbers whose sum is less than 42:
First set = (1,3,5,7) Sum = Second set = ( 3 , 5 , 7 , 9 ) Third set = ( 5 , 7 , 9 , 11 ) Fourth set = ( 7 , 9 , 11 , 13 ) | Where |
So, there are possible 4 odd integers whose sum is less than 42 are:
(1,3,5,7) , (3,6,7,9,) , (5,7,9,11) , (7,9,11,13)
Thus, the set of 3 positive odd numbers are (1,3,5,7) , (3,6,7,9,) , (5,7,9,11) , (7,9,11,13)
Chapter 5 Solutions
Algebra 1
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