SOLUTION: just need help with this word problem. how do we write out an equation from consecutive odd and even word problems? can you give an example?

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Question 145478: just need help with this word problem. how do we write out an equation from consecutive odd and even word problems? can you give an example?
Found 2 solutions by vleith, ankor@dixie-net.com:
Answer by vleith(2983) (Show Source):
You can put this solution on YOUR website!
For problems like this, let n be the lowest number. Then let n+2, n+4, etc be the 'next consecutive' integers.
An example, three consecutive even integers have an average of 10, what are they?

so n+2 = 10 and n+4 = 12
8,10,12

Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website!
just need help with this word problem. how do we write out an equation from consecutive odd and even word problems? can you give an example?
:
"Three consecutive even integers are such that the square of the third is 76
more than the square of the second"
:
Break it down as follows:
:
Three consecutive even integers:
x, (x+2), (x+4)
:
are such that the square of the third is 76 more than the square of the second.
(x+4)^2 = (x+2)^2 + 76
FOIL
x^2 + 8x + 16 = x^2 + 4x + 4 + 76
:
Arrange the x's on the left and the numbers on the right:
x^2 - x^2 + 8x - 4x = 4 + 76 - 16
:
4x = 64
x =
x = 16 is the 1st even integers
:
Find the three integers.
16, 18, 20
:
:
Check solution in the statement:
"square of the third is 76 more than the square of the second."
20^2 = 18^2 + 76
400 = 324 + 76; confirms our solution
: