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Math Question

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A rectangular piece of metal is 25 in longer than it is wide. Squares with sides

5in long are cut from the four corners and the flaps are folded upward to form an open box. If the volume of the box is 750in cubed3โ,what were the original dimensions of the piece ofโ metal?

What is the original width?   in

yojaymarojas  May 13, 2017

#1
+5552
+4

Imagine folding this up like it says in the problem...we can see that

height of box = 5

width of box = w - 5 - 5 = w - 10

length of box = (w + 25) - 5 - 5 = w + 15

volume of box = (height)(width)(length)

750 = (5)(w - 10)(w + 15)

750/5 = (w - 10)(w + 15)

150 = w2 + 5w - 150

0 = w2 + 5w - 300

0 = (w + 20)(w - 15)

w = -20     or     w = 15

So...the original width must be 15 in.

hectictar  May 13, 2017
Sort:

#1
+5552
+4

Imagine folding this up like it says in the problem...we can see that

height of box = 5

width of box = w - 5 - 5 = w - 10

length of box = (w + 25) - 5 - 5 = w + 15

volume of box = (height)(width)(length)

750 = (5)(w - 10)(w + 15)

750/5 = (w - 10)(w + 15)

150 = w2 + 5w - 150

0 = w2 + 5w - 300

0 = (w + 20)(w - 15)

w = -20     or     w = 15

So...the original width must be 15 in.

hectictar  May 13, 2017

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