Question 1012360
<pre>
Let: A = Allen's age NOW

Let: B = Ben's age NOW

Then: A-7 = Allen's age 7 years ago

And: B-7 = Ben's age 7 years ago.

Also: one-half as old as Ben was then = {{{1/2}}}(B-7)

And: 16 years more than one- half as old as Ben was then =

{{{1/2}}}(B-7)+16
</pre>
" The sum of Allan and Ben's age is 45.
<pre>
A + B = 45
</pre>
Seven years ago, Allan was 16 years more than one- half as old as Ben was then.
<pre>
A-7 = {{{1/2}}}(B-7)+16

So the system of equations is

{{{system(A+B=45,A-7=expr(1/2)(B-7)+16)}}}

Simplify the second equation, first by multiplying
both sides by 2:

{{{red(2)*(A-7)=red(2)*expr(1/2)(B-7)+red(2)*16}}}

{{{2A-14=1(B-7)+32}}}

{{{2A-14=B-7+32}}}

{{{2A-14=B+25}}}
{{{2A-B=39}}}

Now solve the system of equations:

{{{system(A+B=45,2A-B=39)}}}

Edwin</pre>