SOLUTION: . A cabinet has two sliding doors of different sizes. When the cabinet is fully closed, they overlap by two-fifths of the width of the smaller door. When both doors are slid to o

Question 1151693: . A cabinet has two sliding doors of different sizes. When the cabinet is fully closed,
they overlap by two-fifths of the width of the smaller door. When both doors are
slid to one side, the part of the longer door that is not behind the shorter one is
half as wide as the original overlap, and the open portion of the cabinet is 36
inches wide. What is the width of the whole cabinet?

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
let T = the total width of the cabinet.
let S equal the length of the shorter door.
let L equal the length of the longer door.

when the doors are shut, then the overlap is 2/5 * S.
therefore T = S + L - 2/5 * S.
this makes T = 3/5 * S + L

when the doors are open, T = L + 36

since T = L + 36 and T = 3/5 * S + L, then:
L + 36 = 3/5 * S + L
subtract L from both sides of this equation to get:
36 = 3/5 * S
solve for S to get:
S = 5/3 * 36 = 60

when the doors are open, you also get L = S + 1/5 * S.
since S = 60, this means that L = 60 + 12 = 72

you now have S = 60 and L = 72
when the doors are closed, you get T = S + L - 2/5 * S
this becomes T = 60 + 72 - 24.
this makes T = 108

when the doors are open, you get T = L + 36.
since L = 72, this becomes T = 72 + 36
this makes T = 108.

when the doors are open, you get T = S + 1/5 * S + 36
since S = 60, this becomes T = 60 + 12 + 36.
this makes T = 108

the numbers check out.

the length of the shorter door is 60 inches.
the length of the longer door is 72 inches.
the length of the cabinet is 108 inches.

this can be visualized in the following display.

$$$

the very top line that is not labeled was an error and should be ignored.

your solution is that the length of the cabinet is 108 inches.

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