Question 654844: Please help! I'm trying to help my little brother on his math and ive been working with him for hours and these last few have me lost, and my brain can no longer work. Would really love your help.
1. The lesser of two consecutive even integers is 10 mor than one-half the greater. Find the integers
2. The greater of two consecutive even integers is 6 less than three times the lesser. Find the integers.
3. Find the consecutive integers such that twice the sum of the two greater integers exceeds times the first by 91.
4. Find a set of four consecutive positive integers such that the greatest integer in the set is twice the least integer in the set.
Answer by DrBeeee(684)   (Show Source):
You can put this solution on YOUR website! I suggest you look at other consecutive interger problem solved by DrBeeee.
They are straight forward.
1. Let n = the smaller integer, then the next even integer is
equal to n+2. Make sense? For example if the first intger is 18 the next one is 20 or 18+2.
Your first problem states that
(1) n = 10 + (n+2)/2, agree?
All we need to do is simplify (1),
Multiply both sides by 2 (I hate fractions) to get
(2) 2*n = 20 + n + 2 or
(3) n = 22
Then the next number is 24. Right? How do we know? Check with (1).
Is (22 = 10 + (22+2)/2)?
Is (22 = 10 + 24/2)?
Is (22 = 10 + 12)?
Is (22 = 22)? Yes
Answer: The two consecutive even integers are 22 and 24.
Note that we don't have to worry about whether or not n is even or odd, the problem statement satisfies that condition.
Let's do your next problem.
2. This statement is
(2) n + 2 = 3*n - 6
Simplify and solve (2) for n,
(3) 2 + 6 = 3n - n or
(4) 2n = 8 or
(5) n = 4, then the next even integer is 6
Let's check with (2).
Is (4 + 2 = 3*4 - 6)?
Is (6 = 12 - 6)?
Is (6 = 6)? Yes
Answer: The two consecutive even integers are 4 and 6
I think you get it. Good luck with 3. and 4.
I can't help you on 3. because we don't know how any times etc. The answer to 4. is 6,8,10,12.
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