Question 930613
<pre>
Let the two even numbers be n and n+2.  Then translating the
words,

{{{expr(1/2)(n^""+(n+2))}}}{{{"">=""}}}{{{expr(1/4)(n+2)+15}}}

Multiply both sides by 4 to clear of fractions:

{{{4*expr(1/2)(n^""+(n+2))}}}{{{"">=""}}}{{{4*expr(1/4)(n+2)+60}}}

{{{2(n^""+(n+2))}}}{{{"">=""}}}{{{n+2}+60}}

{{{2(n+n+2)}}}{{{"">=""}}}{{{n+2+60}}}

{{{2(2n+2)}}}{{{"">=""}}}{{{n+62}}}

{{{4n+4}}}{{{"">=""}}}{{{n+62}}}

{{{4n+4}}}{{{"">=""}}}{{{n+62}}}

{{{3n}}}{{{"">=""}}}{{{58}}}

{{{n}}}{{{"">=""}}}{{{19&1/3}}}

So the first even number n could be is 20

So the two consecutive even numbers are 20 and 22. 

-------

Checking:

We need to find half of the sum of the two 
consecutive even numbers.

Their sum is 20+22 or 42

Half their sum is 21

That must be at least 15 more than a quarter of the second number

A quarter of the second number is {{{22/4}}} or {{{5&1/2}}}

Is 21 at least 15 more than {{{5&1/2}}}?  Yes it is, for {{{21-5&1/2}}}
is {{{15&1/2}}} so 21 is {{{15&1/2}}} more than {{{5&1/2}}}.

So it checks.  Are 20 and 22 the least?

Let's try 18 and 20.

Their sum is 18+20 or 38

Half their sum is 19

That must be at least 15 more than a quarter of the second number

A quarter of the second number is {{{19/4}}} or {{{4&3/4}}}

Is 19 at least 15 more than {{{4&3/4}}}?  No it is't, for {{{19-4&3/4}}}
is {{{14&1/4}}} so 19 is only {{{14&1/4}}} more than {{{4&3/4}}}.

So it doesnt check.  So 20 and 22 are the least.

Answer 20 and 22.

Edwin</pre>