Find the sets of all three consecutive even positive integers with a sum no greater than 36.
Answer to Problem 42PPS
The set of 3 positive even numbers are (2, 4, 6); (4, 6, 8); (6, 8, 10); (8, 10, 12)
Explanation of Solution
Given: Find the sets of all three consecutive even positive integers with a sum no greater than 36.
Concept Used:
Difference of consecutive even integers is 2.
Condition: Sum of all three consecutive even positive integers no greater than 36.
Let the least positive even number be x , the other two are:
Their sum:
Equation:
Calculation:
Equation:
Solve for x, the least number of the set.
So, the least positive even number be no more than 10.
All possible set of four odd numbers whose sum is less than 42:
First set = (2, 4, 6) Sum = Second set = ( 4, 6, 8 ) Sum = Third set = (6, 8, 10) Sum = Fourth set = ( 7 , 9 , 11 , 13 ) Sum = | Where (the first positive even integers less than 10. Any number less that 10 would satisfy the condition. ) |
The set of all 3 positive even numbers whose sum is no more than 42 are:
(2, 4, 6); (4, 6, 8); (6, 8, 10); (8, 10, 12)
Thus, the set of 3 positive even numbers are (2, 4, 6); (4, 6, 8); (6, 8, 10); (8, 10, 12)
Chapter 5 Solutions
Algebra 1
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