Word Problem

[Guest]

Please help with this word problem
A box (rectangular/no top) is to have a volume of 64 cubic meters. The width of the base must be 4 meter to insert into a vault. When trimmed to size, material cost $12.00 per square meter for the base and $6.00 per square meter for the sides. What is the cost for the box?

Please help!
Thanks

 

[stapel]

What variables have you chosen for the length and height of the box?

Please reply showing all of your steps so far.

Thank you.

Eliz.

 

[Guest]

This is what I have so far:
w=4m, h=height L =length

4*h*d =64, this is for volume

The area of the base is 4*L (length)
there for the area of the sides is (2*6*L)h

Okay, this is where I get loss

 

[stapel]

h=height L =length 4*h*d =64

Okay, but what does "d" stand for?

The area of the base is 4*L (length)

Agreed. Now what is the cost for that area?

there for the area of the sides is (2*6*L)h

There are four sides, two of one size and two of another (unless the length turns out, in the end, to equal the width). What do the "2" and the "6" stand for in your above expression?

Try labelling clearly and working orderly:

. . . . .width: 4
. . . . .length: L
. . . . .height: h

. . . . .volume: 4Lh = 64 (given volume)

. . . . .Then Lh = 16, so L = 16/h.

. . . . .base area: 4L = 4(16/h) = 64/h

. . . . .cost of base: 12(64/h) = ....

...and so forth.

Eliz.