Question 1092130
L = the length of the picture
w = the width of the picture
:
A framed picture is 7 inches longer than wide.
L = w + 7
 The width of frame is 5 inches. Total area is 470 square inches
This would add 10 inches to both length and width
(L+10)*(w+10) = 470
Replace L with (w+7)
((w+7)+10)*(w+10)
(w+17)*(w+10) = 470
FOIL
w^2 + 10w + 17w + 170 = 470
w^2 + 27w + 170 - 470 = 0
w^2 + 27w - 300 = 0
Using the quadratic formula, the positive solution 
w = 8.46 in is the width of the picture
then
L = 8.46 + 7 = 15.46 in is the length of the picture
 " Determine outside dimensions of framed picture.
Add 10" to each dimension
25.46" by 18.46" the overall dimensions
:
:
:
Check 25.46 * 18.46 = 469.99 ~ 470