Question 520926: Three consecutive even integers are such that the difference of the smallest integer and twice the largest integer is 10. Find the three integers.
Found 2 solutions by jlshires, lwsshak3:
Answer by jlshires(17)   (Show Source):
You can put this solution on YOUR website! The key to solving this problem is that you know the integers are consecutive, even integers.
The smallest you can set as x. therefore:
Let the smallest integer = x
Let the middle integer = x+2
Let the largest integer = x+4
this will make them the consecutive even numbers. (ex: 2,4,6 or 8,10,12)
The difference of the smallest integer and twice the largest integer is 10
twice the largest would equal 2(x+4) Therefore:
2(x+4)-x = 10
multiply out the 2
2x+8-x=10
combine like symbols (2x-x=x)
x+8=10
subtract 8 from both sides
x=2
Substitute x back into the original formulas
x=2
x+2=4
x+4=6
the numbers are 2, 4, 6
(**Always put the numbers that you find back into the formula that you created to test your answer. ex: For this problem, but 2 and 6 back into the formula for "the difference between the smallest and two times the largest equals 10.
this would be (2*6)-2 = 12-2 = 10)
Answer by lwsshak3(11628) (Show Source):
You can put this solution on YOUR website! Three consecutive even integers are such that the difference of the smallest integer and twice the largest integer is 10. Find the three integers.
**
let x=smallest even integer
x+2=next consecutive even integer
x+4=largest of 3 consecutive even integers
..
2(x+4)-x=10
2x+8-x=10
x=10-8=2
x=2
x+2=4
x+4=6
ans:
Three consecutive even integers are: 2, 4 & 6
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