Question 1159323: A picture frame holds an 8-inch by 10-inch photograph. The frame adds a border x inches wide around three sides of the photo. On the fourth side, the frame is wider to accommodate a decoration on the frame. The forth side is (3x-1) inches wide, as shown in the figure.
a) write a quadratic expression for the combined area of the frame in terms of x.
b)if the border on the three matching sides in 1 inch, what is the combined area of the frame?
c)if the combined area of the frame is 165 square inches, find x.
Found 2 solutions by MowMow, ikleyn:
Answer by MowMow(42)   (Show Source):
Answer by ikleyn(52778)  (Show Source):
You can put this solution on YOUR website! .
A picture frame holds an 8-inch by 10-inch photograph. The frame adds a border x inches wide around three sides
of the photo. On the  fourth side, the frame is wider to accommodate a decoration on the frame.
The fourth side is (3x-1) inches wide, as shown in the figure.
(a) write a quadratic expression for the combined area of the frame in terms of x.
(b) if the border on the three matching sides in 1 inch, what is the combined area of the frame?
(c) if the combined area of the frame is 165 square inches, find x.
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(a) The Figure is not shown, so the reference to the Figure is empty (carries zero information).
@MowMow assumes that the fourth side of (3x-1) inches wide is the 8 inches long.
I will follow to this assumption in order to show that the "solution" by @MowMow is inadequate.
Indeed, then the outer dimensions of the frame are (10+x+(3x-1)) = (9+4x) inches by (8+2x) inches,
which is DIFFERENT from (10+3x) and (8+2x) inches, used in the post by @MowMow.
Then the quadratic expression for the combined area of the frame should be different from that
in the post by @MowMow.
As the request (a) is presented in the post, it baffles me.
If they request for the area of the large rectangle with the sides (9+4x) and (8+2x),
then the area is the product (9+4x)*(8+2x) square inches.
If they want the area of the frame only, then this area is (9+4x)*(8+2x) - 8*10 square inches.
Actually, the request in (a) is written in such an uncertain way, that the precise meaning
is unclear. It is not a way to write a Math problem.
(b) When I read the request (b), it baffles me again.
Indeed, it says that the border of the three matching sides is 1 inch, but says nothing about the fourth side.
In any case, the answer by @MowMow is irrelevant.
(c) The same uncertainty is with the request (c).
From their formulation, it is unclear, if we are under condition (a) or under condition (b).
As a final resume, my opinion is that
(a) this writer, who created the problem, is not able to generate a Math problem
by an non-ambiguous way, as it is required for Math problems.
(b) this post is not an adequate Math problem and can not be considered as a correct Math problem.
(c) For any interpretation, the solution and the answers by @MowMow are incorrect.
For a reader, my advice is to ignore this post as inaccurate and ambiguous
and to ignore the "solution" by @MowMow as inadequate.
I know that all solutions and all posts are included into databases for artificial intelligence.
So I want to warn: DO NOT INCLUDE IT in the database for AI, in any form.
Simply re-direct it into the garbage bin, where its right place should be.
The author of this problem deserves a big minus and a serious warning
for unprofessionalism in writing Math problems.
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