Question
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?
Supposedly the answer is y=h, but the way it is told is hard to understand. Can someone please explain?
Answers
AshBlueRaven
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 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.
AshBlueRaven
The answer is y=h. But I don't know how to find it.
jaffit
oh you need an explanation for it how you got that answer.
AshBlueRaven
It told me the answer and explained how to get it but I don't understand it.
AshBlueRaven
First, it told me to do this for the first suitcase by finding volume, V = lwh. V= (3y)(2y – 1)(y/3)
jaffit
oh you dont understand it
AshBlueRaven
Correct.
Reiny
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 , <b>NOT h = y</b>
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 , <b>NOT h = y</b>
jaffit
thank you
jaffit
thx
AshBlueRaven
See, this is what I figured as well, but the instructions say to originally change the y, the ones by themselves, to a y/2 for the second and y/3 for the first. I don't understand why it would change them.
henry2,
V1 = V2.
3y * (2y-1) * y = (4y-2) * y * h.
3y * (2y-1) * y = 2(2y-1) * y * h,
Divide both sides by y(2y-1):
3y = 2h,
h = 3y/2 = (3/2)y.
3y * (2y-1) * y = (4y-2) * y * h.
3y * (2y-1) * y = 2(2y-1) * y * h,
Divide both sides by y(2y-1):
3y = 2h,
h = 3y/2 = (3/2)y.