Expert: Paul Klarreich - 9/11/2007

Question
find two consecutive even integers such that six times the first equals five times the second

Answer
Questioner:   Karaese Smith
Category:  Advanced Math
Private:  No
 
Subject:  Consecutive integers
Question:  find two consecutive even integers such that six times the first equals five times the second
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Hi, Karaese,

The basic scheme is:

If you have consecutive integers, you represent:

x     = the first integer.
x + 1 = the second integer.

But here you have something a little different:

If you have consecutive integers OF THE SAME PARITY, you represent:

x     = the first  (odd/even) integer.
x + 2 = the second (odd/even) integer.

Strange, isn't it?  You represent the second as  x + 2, whether you are talking about even or odd integers.  You will probably have to lie down for a while and recover from this.

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OK, your problem:

Find two consecutive even integers such that six times the first (even integer) equals five times the second (even integer).

x     = the first  (odd/even) integer.
x + 2 = the second (odd/even) integer.

Now your sentence says:

six times the first (even integer) equals five times the second (even integer).

six times ............ x .........    =   five times ......(x + 2)...........

6x = 5(x + 2)

6x = 5x + 10

x = 10

The first even integer is 10.
The second even integer is 10 + 2 = 12.