SOLUTION: The sum of the second and the fourth even integers is 49 more than one-fourth of the third integer. What are these four consecutive integers?

Question 1109247: The sum of the second and the fourth even integers is 49 more than one-fourth of the third integer. What are these four consecutive integers?
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
let x be the first even number then we can list the four even integers as
:
x, x+2, x+4, x+6
:
now we can write the relationship
:
(x+2 + x+6) = ((x+4)/4) + 49
:
now simplify the expression
:
2x +8 = ((x+4)/4) + 49
:
multiply both sides of = by 4
:
8x +32 = x+4 +196
:
7x +32 = 200
:
7x = 168
:
x = 24
:
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the four even numbers are 24, 26, 28, 30
:
check the answer
:
26 + 30 = (28/4) + 49
:
56 = 7 + 49
:
56 = 56
:
answer checks
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