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?
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?