How do I solve it?

Question

a rectangular piece of metal is 25in longer than it is wide. Squares with sides 5 in 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 3000 in what were the original dimensions of the piece of metal?

Answer 1

Let's start with what we know. If we let the width be W, we know the length is 25 more than the width, or 25+W. Whenever we make the box, we cut 5 x 5 squares from each corner, so we know each side is 5 less than it was before it got turned into the box. So, we know that the width is W-5, the length is W+25-5 (or W+20), and the depth or height is 5.

Because the volume is given as 3000 and we know the volume of a rectangular prism to be length x width x height, we know that 3000 = (W-5)(W+20)(5)

Let's solve for W! Start by dividing both sides by 5 to get

600 = (W-5)(W+20)

Multiply your two terms together using FOIL to get

600 = W^2 - 5W + 20W - 100

Collect like terms to get

600 = W^2 +15W - 100

Subtract 600 from both sides to get

W^2 +15W - 700 = 0

Factor your quadratic equation, knowing you need two numbers that add to positive 15 and multiply to -700 to get

(W + 35)(W - 20) = 0

Set both terms equal to 0 and solve to get the two answers

W = 20 & -35

Because our original width of our rectangle can't be -35, we know the original width must have been 20. We know the original length must have been 25 more than that, or 45. Therefore, the original dimensions were 20 x 45.

Answer 2

w represents the width of the piece

w + 25 represents the length of the piece

w - 10 represents the width of the box

w + 15 represents the length of the box

3000 = (w + 15)(w -10)(5)

Can you solve for w and answer?