Math CentralQuandaries & Queries


Question from cassandra, a student:

find 2 consecutive even integers whose sum is 34

find 3 consecutive even integers such that 3 time the middle interger
is 10 more than the greatest.

Hi Cassandra,

To answer these, we need to understand what is meant by consecutive even integers. By this we mean, integers which are divisible by two, and which "follow" each other. For instance, 2 and 4 are consecutive even integers because both numbers are integers, divisible by two, and 4 is the next even integer larger than 2. Similarly, 14 and 16, 8 and 10, 100 and 102, are also examples of consecutive even integers. Your question is to find two such numbers which happen to add to 34. To do this, we let a variable, n, be the smaller integer. Then our other number is (n+2)[can you see why?]. So your question amounts to the following, n + (n+2) = 34.

Your second question uses the same idea. If 'n' is your first integer, what form does the middle one have? What form does the greatest one have?


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