Question

The design of a digital box camera maximizes the volume while keeping the sum of the dimensions at 6 inches. If the length must be 1.5 times the height, what should each dimension be?
Hint: Let x represent one of the dimensions, and then define the other dimensions in terms of x.

if you could help me work it out that would be great. I really don't understand.

Answer 1

calculus?

Answer 2

Algebra 2

Answer 3

do you know the formula for the volume of a "box"?

Answer 4

L * w * h

Answer 5

Let x represent one of the dimensions. which one do you want to call x ?

Answer 6

Um, height?

Answer 7

or maybe, first analyze what we know.
length must be 1.5 times the height
can you write a formula that shows this ? Give it a try.

Answer 8

(1.5)L

Answer 9

you should be writing an equation (which has an = sign in it)

start by renaming the words with their "short names": length is L and height is H:
length must be 1.5 times the height
L is 1.5 * H

can you change that into an equation ?

Answer 10

1.5H=L

Answer 11

Yes, that is good.

Answer 12

now let's tackle this part:
sum of the dimensions at 6 inches

can you write an equation for this?

Answer 13

L+W+H=6

Answer 14

ok, good

Answer 15

now if we call H "x" (yet a new name for height)
we have
H= x
L= 1.5 H
so what is L (if we use x instead of H ) ?

Answer 16

1.5x?

Answer 17

yes, but get used to writing the whole equation (less chance of getting confused)
L = 1.5

so here is what we have (so far):

H= x
L= 1.5 x
H+L+W= 6

can you replace H and L in the last equation (H+L+W= 6) so we have x's ?

Answer 18

**yes, but get used to writing the whole equation (less chance of getting confused)
L = 1.5x

Answer 19

Okay, x+1.5x+W=6

Answer 20

yes.
can you solve for W ?

Answer 21

One sec