Question 1050741
<b>Anton is four years older than Lisa. The product of his 
age 3 years from now and Lisa 's age two years ago is 90 
years. Find their present age. 
<pre>
Lisa's present age = L
</pre>
Anton is four years older than Lisa.
<pre>
Anton's present age = L+4
Anton's age 3 years from now = (L+4)+3 = L+4+3=L+7
Lisa's age 2 years ago = L-2
</pre>
The product of his age 3 years from now and Lisa's age two years ago is 90 years
<pre>
{{{matrix(1,7,
(matrix(8,1,"Anton's",age,3,years,from,"now,",or,(L+7))),
"×",
(matrix(7,1,"Lisa's",age,2,years,"ago,",or,(L-2))),
"",
""="",
"",
90)}}}

{{{(L+7)(L-2)}}}{{{""=""}}}{{{90}}}

Use FOIL on the left

{{{L^2+5L-14}}}{{{""=""}}}{{{90}}}

Get 0 on the right by subtracting 90 from both 
sides:

{{{L^2+5L-104}}}{{{""=""}}}{{{0}}}

The factor pairs that have product 104 are

104×1, 52×2, 26×4, 13×8

Only 13 and 8 have difference 5.  So we factor

{{{(L+13)(L-8)}}}{{{""=""}}}{{{0}}}

L+13 = 0;     L-8 = 0
   L = -13      L = 8

Ignore the negative answer.

Lisa's present age = L = 8

Anton's age = L+4 = 8+4 = 12

{{{matrix(1,7,
(matrix(8,1,"Anton's",age,3,years,from,"now,",or,12+3=15)),
"×",
(matrix(7,1,"Lisa's",age,2,years,"ago,",or,8-2=6)),
"",
""="",
"",
90)}}}

And indeed 15×6 = 90.

Edwin</pre></b>