A flight attendant packed two rectangular suitcases for her trip to Hawaii. Both hold the same volume of clothes. Her brown suitcase has a length of 3y, a width of 2y – 1, and a height of y. Her black suitcase has a length of 4y − 2 and a width of y. What is a simplified expression for the height of the black suitcase in terms of y?
Supposedly the answer is y=h, but the way it is told is hard to understand. Can someone please explain?
The volume of each rectangular suitcase in the problem above can be found using the formula V=lwh. Substitute the rational expressions from the original problem to set up an equation.
The volume for the first suitcase would be:
V = lwh
V= (3y)(2y – 1)()
The volume for the second suitcase would be:
V = lwh
V = (4y – 2)()(h)
Since both suitcases must hold an equal volume, set the two sides equal to one another. Then solve for h to find an expression representing the height of the black suitcase.
3y times (2y minus 1) times y over 3 = (4y minus 2) times y over2 times h
2 y cubed minus y squared = 2 y squared minus y times h
(2 y cubed minus y squared) over (2 y squared minus y) = h
If possible, factor and reduce.
The answer is y=h. But I don't know how to find it.
oh you need an explanation for it how you got that answer.
It told me the answer and explained how to get it but I don't understand it.
First, it told me to do this for the first suitcase by finding volume, V = lwh. V= (3y)(2y – 1)(y/3)
oh you dont understand it
Correct.
volume of first: (3y)(2y - 1)(y) = 3y^2(2y-1)
let the height of the 2nd be h
volume of second = h(y)(4y - 2) = hy(2)(2y-1) = 2hy(2y-1)
But, they are the same, so
2hy(2y-1) = 3y^2(2y-1)
divide both sides by 2y-1
2hy = 3y^2
divide both sides by y
2h = 3y
h = (3/2)y , NOT h = y