Problema Solution
Sandy purchases an entertainment center on clearance at 65% off that has an opening measuring 42 inches by 20.5 inches. If widescreen TVs (16:9 aspect ratio) are on sale at the local electronics store for the next 3 days, what is teh max screen size that Sandy should purchase assuming that each screen has a 1 inch wide frame bordering the screen?
Answer provided by our tutors
let
x = length of the screen
y = width of the screen
w = 1 in wide frame
since the aspect ratio is 16:9 we have
x : y = 16 : 9
x = 16y/9
the limitation for length is 42 inches
the length of the screen is x + 2w (the length + the frame) and it should fit in the opening that's why
x + 2 < 42
the width of the screen is y + 2w (the width + the frame) and it should fit in the opening that's why
y + 2 < 20.5
by solving the system of inequalities
16y/9 + 2 < 42
y + 2 < 20.5
we find
y < 18.5 then x < 16*18.5/9 = 32.89
y < 22.5 then x < 16*22.5/9 = 40
Sandy should purchase the screen that is 32.89 in long and 18.5 in wide.