<PRE><B>Question 1092172</B>
L = the length of the frame
w = the width of the frame
:
A framed picture is 7 inches longer than wide.
L = w + 7
 The width of frame is 5 inches.  The frame area is 470 square inches
then
(L-10 = length of the picture
and
(w-10) = width of the picture
:
Overall area - picture area = 470 sq/in
L*w - ((L-10)*(w-10)) = 470
replace L with (w+7)
w(w+7) - (((w+7)-10)*(w-10)) = 470
w^2+7w - ((w-3)*(w-10)) = 470
FOIL
w^2 + 7w - (w^2 - 10w - 3w + 30) = 470
w^2 + 7w - (w^2 - 13w + 30) = 470
removing the brackets changes the signs
w^2 + 7w - w^2 + 13w - 30  = 470
Combine like terms
20w - 30 = 470
20w = 470 + 30
20w = 500
w = 500/20
w = 25 inches is the width of the frame
then
L = 25 + 7 = 32 inches is the length
 &quot; Determine outside dimensions of framed picture.&quot;
32 by 25 inches
:
;
:
Confirm this, find the overall are and the picture area
32 * 25 = 800
22 * 15 = 330
-------------
difference 470
</PRE>