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Question 182113: Q.((( If three times the smaller of two consecutive even integers is added to the larger, the result is 4 more than three times the larger. Find the two numbers (solve algebraically))).
Answer by MathGuyJoe(20)   (Show Source):
You can put this solution on YOUR website! Let x = smaller even number. That means (x + 2) will be the next consecutive even number (aka. 'larger' in the word problem).
Now, write the statements down in equation form (substitute x and (x+2) in place of the two numbers):
"Three times the smaller of two consecutive even integers is added to the larger,":
3x + (x + 2)
"The result is 4 more than 3 times the larger.":
= 4 + (3 * (x + 2) )
So putting it all together we have:
3x + (x + 2) = 4 + (3 * (x + 2))
Simplifying (remember to multiply the '3' by both the 'x' and the '2' on the right hand side):
4x + 2 = 4 + 3x + 6
Gathering the x's on the left (subtract 3x from both sides):
1x + 2 = 10
Subtracting 2 from both sides gives us x = 8, which represents the smaller even number. Given that, we know that the next consecutive even number would be 10.
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