SOLUTION: find four consecutive odd integers so that the sum of the smallest integer and the largest integer is the same as the sum of all four integers
Question 338605: find four consecutive odd integers so that the sum of the smallest integer and the largest integer is the same as the sum of all four integers Found 3 solutions by Alan3354, Stitch, CharlesG2:Answer by Alan3354(69443) (Show Source):
You can put this solution on YOUR website! The integers are n, n+2, n+4 and n+6
n + n+6 = n + n+2 + n+4 + n+6
2n+6 = 4n + 12
-2n = 6
n = -3
--> -3, -1, 1, 3
You can put this solution on YOUR website! Set Up:
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Equation 1:
Let A = X
Let B = X + 2
Let C = X + 4
Let D = X + 6
Solution:
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Rewrite the equation
Equation 1:
Combine like terms
Subtract 2X from both sides Subtract 12 from both sides Divide both sides by 2
Now substitute -3 into the Lettter variable equations for X
A = X
B = X + 2
C = X + 4
D = X + 6
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A = -3
B = -3 + 2
C = -3 + 4
D = -3 + 6
Simplify
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A = -3
B = -1
C = 1
D = 3
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Now check the answers into equation 1
Equation 1:
You can put this solution on YOUR website! find four consecutive odd integers so that the sum of the smallest integer and the largest integer is the same as the sum of all four integers
4 consecutive odd integers: n, n + 2, n + 4, n + 6
sum of smallest integer and largest integer: n + n + 6 = 2n + 6
sum all 4 integers = n + n + 2 + n + 4 + n + 6 = 4n + 2 + 4 + 6 = 4n + 12
2n + 6 = 4n + 12
-2n = 6
n = -3
-3, -1, 1, 3
check:
sum of smallest and largest = -3 + 3 = 0
sum of all 4: -3 + -1 + 1 + 3 = -4 + 4 = 0
the sums are the same
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