SOLUTION: the height of a photo is 4 inches more than its width. After enlargement the height will increase by 18 inches and the width by 12 inches. If the ratio of the area of the original

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Question 186725: the height of a photo is 4 inches more than its width. After enlargement the height will increase by 18 inches and the width by 12 inches. If the ratio of the area of the original photo to the area of the enlarged photo is 4:25, then what will the new dimensions of the pgoto become? thank you
Answer by ankor@dixie-net.com(22740) (Show Source):
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the height of a photo is 4 inches more than its width. After enlargement the
height will increase by 18 inches and the width by 12 inches.
If the ratio of the area of the original photo to the area of the enlarged
photo is 4:25, then what will the new dimensions of the photo become?
:
Let x = the width of the photo
and
(x+4) = the height
then
Area = x(x+4) = (x^2 + 4x)
:
"After enlargement the height will increase by 18 inches and the width by 12 inches."
(x+4+18) = (x + 22) is the height after enlargement
and
(x+12) = width after enlargement
then
Area = (x+22) * (x+12) = (x^2 + 34x + 264)
;
If the ratio of the area of the original photo to the area of the enlarged photo is 4:25,
=
Cross multiply
25(x^2 + 4x) = 4(x^2 + 34x + 264)
:
25x^2 + 100x = 4x^2 + 136x + 1056
:
25x^2 - 4x^2 + 100x - 136x - 1056 = 0
:
21x^2 - 36x - 1056 = 0
:
7x^2 - 12x - 352 = 0
:
use the quadratic formula: a=7, b=-12, c=-352
You should get a positive solution of x = 8
:
The enlarged dimensions:
8 + 22 = 30" is the height
8 + 12 = 20" is the width
;
:
Check solution:
= =