SOLUTION: A rectangular canvas picture measures 10 inches by 32 inches. The canvas is mounted inside a frame of uniform width, increasing the total area to 504 inches. Write an equation t

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Question 1086606: A rectangular canvas picture measures 10 inches by 32 inches. The canvas is mounted inside a frame of uniform width, increasing the total area to 504 inches.
Write an equation to model this situation, and find the uniform width of the frame.
Found 2 solutions by ikleyn, josgarithmetic:
Answer by ikleyn(52943) About Me  (Show Source):
You can put this solution on YOUR website!
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If x is the uniform width of the frame, then the dimensions of the larger rectangle are (10 + 2x) and (32 + 2x).


To find "x", you need to solve the "area" equation

(10 + 2x)*(32 + 2x) = 504.


You can solve it by any method you want/ you know.


I will solve it MENTALLY by my own method:


I will factor (mentally) 504 into the product of two factors that differ in 32-10 = 22:


504 = 14*36.


Hence, 10 + 2x = 14  and 2x = 14 - 10 = 4.  Then  x = 2.

Answer. The wide of the frame is 2 inches.



Answer by josgarithmetic(39632) About Me  (Show Source):
You can put this solution on YOUR website!
Frame is AROUND the picture.

%2810%2B2x%29%2832%2B2x%29=504
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2%285%2Bx%29%282%29%2816%2Bx%29=4%2A126
%28x%2B5%29%28x%2B16%29=126------the two factors on the left side differ by 11.

126=2%2A63=3%2A42=6%2A21=7%2A18
notice 18-7=11

If x+5=7, then x=2.
If x+16=18, then x=2.
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You could also start from %28x%2B5%29%28x%2B16%29=126 and solve the quadratic equation.