Dimensions of Boxes

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S_100

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A packing company supplies storage boxes in three different sizes: small, medium, and large.
All three types of box have the same ratio of width:length and height:length.
It is noted that:
A. Eight small boxes fit neatly inside one medium box.
B. The length of the small box is the same as the height of the medium box.
C. The base area (i.e. width times length) of a large box is 9 times smaller than the base area of the small box.
D. The lengths of all three boxes added together is 2.4 m.
E. The width of the medium box is twice the height of the small box.

What are the lengths of the three different boxes?

My attempt at a solution:
A : 8(Ls *WS * HS) = LM *WM *HM

B: Ls= HM

C: LL * WL = 9 Ls WS

D: LS + LM + LL =2.4

E: WM = 2HS

I first thought, Need to get like terms for D, to find out the length of one of the boxes.
I noticed E and B can be subsituted into A to get

8(LS *WS * HS) = LM * WM * HM
8(LS *WS * HS) = LM * 2HS * LS

To get 2LM = 8WS

so LM = 4W S

But from here I am unsure how to go about solving to get all three sides. Are there any potential further steps that can be seen?
 
"C. The base area (i.e. width times length) of a large box is 9 times smaller than the base area of the small box. "

Typo?
 
lev888 said:
"C. The base area (i.e. width times length) of a large box is 9 times smaller than the base area of the small box. "

Typo?
Click to expand...
Sorry yes, it should read :
The base area (i.e. width times length) of a large box is 9 times LARGER than the base area of the small box. "
Nevertheless the algebraic equations are interpreted correctly I believe
 
S_100 said:
A packing company supplies storage boxes in three different sizes: small, medium, and large.
All three types of box have the same ratio of width:length and height:length.
It is noted that:
A. Eight small boxes fit neatly inside one medium box.
B. The length of the small box is the same as the height of the medium box.
C. The base area (i.e. width times length) of a large box is 9 times smaller than the base area of the small box.
D. The lengths of all three boxes added together is 2.4 m.
E. The width of the medium box is twice the height of the small box.

What are the lengths of the three different boxes?

My attempt at a solution:
A : 8(Ls *WS * HS) = LM *WM *HM

B: Ls= HM

C: LL * WL = 9 Ls WS

D: LS + LM + LL =2.4

E: WM = 2HS

I first thought, Need to get like terms for D, to find out the length of one of the boxes.
I noticed E and B can be subsituted into A to get

8(LS *WS * HS) = LM * WM * HM
8(LS *WS * HS) = LM * 2HS * LS

To get 2LM = 8WS

so LM = 4W S................................(F)

But from here I am unsure how to go about solving to get all three sides. Are there any potential further steps that can be seen?
Click to expand...
If you divide F by E you

LM/WM = 2........................................(G)

We also know: ..........................All three types of box have the same ratio of width:length and height:length

Where does that take us?
 
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