SOLUTION: Hello, how are you. I understand the concept of this question, however I don't understand why you would cross out the (l) when solving. For example: (10)(2)(L)=(5)(L)(W) 20=5w W

Algebra ->  Customizable Word Problem Solvers  -> Geometry -> SOLUTION: Hello, how are you. I understand the concept of this question, however I don't understand why you would cross out the (l) when solving. For example: (10)(2)(L)=(5)(L)(W) 20=5w W      Log On

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Question 883313: Hello, how are you. I understand the concept of this question, however I don't understand why you would cross out the (l) when solving.
For example: (10)(2)(L)=(5)(L)(W)
20=5w
Why was the (l) crossed out?
Thank you so much!
Tim has a rectangular prism with a length of 1.0 centimeters, a width of 2 centimeters, and an
unknown height. He needs to build another rectangular prism with a length of 5 centimeters and
the same height as the original prism. The volume of the two prisms will be the same. Find the
width, in centimeters, of the new prism
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
You confused some data between your example and your problem to solve.

Let volume v be a constant. Both prisms are volume v.

First Prism:
L = 1.0
w = 2
h = unknown
v=L%2Aw%2Ah
v=%281.0%29%282%29h

Second Prism:
length, x = 5
width, y = unknown
h = unknown
v=xyh
v=5%2Ay%2Ah

Observe I used somewhat different variables assignments than did you because I do not want confusion between dimensions of first and second prisms. You have two equations and THREE unknowns. This can make the question unsolvable.

We know v is the same for both prisms. We also know that h is given as the same for both prisms.

v=highlight%281%2A2%2Ah=5%2Ay%2Ah%29

The factor h on both sides of what became one equation is fortunate.

The factor 1 on the left side is no longer needed, because this number is the factor 1. This is why it can be omitted NOW, for THIS EQUATION. Multiplication by 1 does not change the meaning of an expression or number.

1%2A2%2Ah=5%2Ay%2Ah
2h=5yh
2h%2F5h=5yh%2F5h
%282%2F5%29%28h%2Fh%29=5yh%2F5h, notice also that h%2Fh=1.
2%2F5=y%285%2F5%29%28h%2Fh%29
highlight%28y=2%2F5%29, which was defined or assigned as width of the second prism.


What really happened was that you missed seeing or forgot was the first prism length was 1.0 cm, NOT 10 cm. You would have answered your question with maybe no trouble if you did not miss that.