Question

Can someone help me with my practice questions? I am having trouble with this question.

Answer 1

hello

first of all, we need to work some maths out

assuming the crate has a shape of a square and it forms a cubiod (in order to have uniform sides since only one side is given)

diamension of crate = 27in

convert in = ft

1in = 0.083ft

27in = ?

`\begin{gathered} 1in=0.083ft \\ 27=x \\ \text{cross multiply and solve for x} \\ x=27*0.083 \\ x=2.241ft \end{gathered}`

area of a square = L * L

`\text{area of crate = 2.241}*2.241=5.022ft^2`

area of the crate = 5.022ft^2

now we know the area of the crates

let the numbers of crates to fill the vehicel be represented by x

let the area of the vehicel be represented by a

now to write an inequality for the number of crates that can be filled, we need to also consider that there's a maximum height in which the crates can't surpass.

`a<5.022x+13.5`

i think the answer should be a < 5.022x + 13.5

b

to know if 7 crates can be stacked up vertically, we need to know the height of the cubiod which will correspond to the height of the crate shown in the diagram as 27in

note: we've converted 27in to feet so i won't be doing that again

in that case, the height of each crate = 2.241ft

now to know if 7 crates can stack up, you can just imagine adding seven of the crates up by 2.241 + 2.241+......+7th. however, we can simply just mutilpy 2.241 by 7 to save us time and stress of adding up

`\text{height of 7 crates = 2.241}*7=15.687ft`

from the calculation above, it's impossible for 7 crates to stack up vertically together because they'll exceed the maximum allowed height

since 15.687ft > 13.5ft