SOLUTION: Find 4 consecutive even integers such that the sum of the second and fourth is 76.

Question 206908This question is from textbook Prentice Hall Mathematics: Algebra 2
: Find 4 consecutive even integers such that the sum of the second and fourth is 76. This question is from textbook Prentice Hall Mathematics: Algebra 2

Found 2 solutions by Alan3354, MathTherapy:
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
Find 4 consecutive even integers such that the sum of the second and fourth is 76.
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The 1st one is not relevant. "Find 3 ... such that the 1st + 3rd = 76" is the same problem.
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The easy way:
76/2 = 38
The 2 numbers are just below and just above 38, --> 36 & 40.
So the 4 numbers are 34, 36, 38, 40.
Answer by MathTherapy(10556) (Show Source): You can put this solution on YOUR website!

Let the first even integer be f
Then the 2nd, 3rd, & 4th are f + 2, f + 4, & f + 6, respectively

Since the sum of the 2nd and 4th is 76, then we get: (f + 2) + (f + 6) = 76

2f + 8 = 76

2f = 68

Since the 1st EVEN INTEGER is 34, it follows that the FOUR CONSECUTIVE EVEN INTEGERS are ,, & .

Check:
Sum of 2nd integer and 4th integer is 76
2nd EVEN INTEGER = 36 ; 4th EVEN INTEGER = 40
Sum of 2nd and 4th EVEN INTEGERS is 76 (36 + 40).
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