Explain how you would find the weight of each stacked box if you knew the weight of the bottom box. Find the weight of each box in a stack of 4 boxes

[eddy2017]

Hi, I am retaking this problem I find really interesting. The poster did not show any try so I am gonna try and at least sshow some thoughts. it is a hard one for me, though, but with the counsel and guidance of tutors nothing is hard here. thank you in advance.


A factory stacks boxes according to their weights. To provide stability to the stacks of boxes, heavier boxes are placed at the bottom of the stack, and lighter boxes are placed at the top. However, because of the boxes’ material, a box can only be placed on top of another if its weight is exactly half the weight of the lower box. Also, due to the height of the warehouse ceiling, boxes can only be stacked 4 levels high. The factory director has asked for your help in answering some questions about these boxes.

a. Explain how you would find the weight of each stacked box if you knew the weight of the bottom box. Find the weight of each box in a stack of 4 boxes if the bottom box weighs 10 pounds.
b. Eventually, these stacks of boxes will go onto pallets for shipping. We need to know how much each stack weighs in order to know how many stacks we can put on each pallet, but the bottom boxes do not necessarily weigh 10 pounds. In fact, we don’t know how much they weigh at all! Write and simplify an expression to find the weight of one stack of 4 boxes based on the unknown weight of the bottom box.
c. Each stack needs to weigh less than 100 pounds. Write and solve an inequality to find the maximum weight of the bottom box. What would be the possible range of weights for this box? It may help you to consider a graph of the solution to your inequality.


Let's go with the first one, and see what information they give us:

Boxes can only be stacked on 4 levels.
Its weight is exactly half the weight of the bottom box. , but the bottom boxes do not necessarily weigh 10 pounds. In fact, we don’t know how much they weigh at all

let's see question a)
If the one at the bottom weighs 10 lb then the one on top of it 1 weighs 5 lb and the one on top of this one weighs 2.5(half of 5 lb) and the one the very top weighs 1.25 .

b) how much each stack weighs....

there has to be an equation for this,
any help in the form of tips/directions is appreciated
eddy

this diagram shows it better

level 1------------------1.25
level 2------------------2.5
level 3------------------5lb
level 4-----------------10lb

 

[eddy2017]

1 can think of adding up all these weights
10+5+2,5+1,25=18,75 lbs

but the second item in the question has knocked me for a loop. There should be an equation. Only that I don't know it.lol
I know there is an equation to calculate weight, but it is more related to physics, i guess,
Calculating Weight
All objects on Earth accelerate downward due to gravity at a rate of 9.8 m/s2. Therefore, if you know the mass of an object, you can calculate its weight using this equation:

F = m × 9.8 m/s^2
I don't think it applies to this problem because we dont know the mass of the boxes

 

[eddy2017]

We need to know how much each stack weighs in order to know how many stacks we can put on each pallet, but the bottom boxes do not necessarily weigh 10 pounds. In fact, we don’t know how much they weigh at all! Write and simplify an expression to find the weight of one stack of 4 boxes based on the unknown weight of the bottom box.
???? any help to reason this one out

 

[eddy2017]

the diagram I drew above reminds me of a sequence... but I am not sure.

 

[lev888]

We need to know how much each stack weighs in order to know how many stacks we can put on each pallet, but the bottom boxes do not necessarily weigh 10 pounds. In fact, we don’t know how much they weigh at all! Write and simplify an expression to find the weight of one stack of 4 boxes based on the unknown weight of the bottom box.
???? any help to reason this one out

Look up geometric sequences. In particular, formulate for the nth term and the sum of n terms.

 

[JeffM]

Eddy

What is unknown? As the great Khan would say, what is the find?

ASSIGN A PRONUMERAL TO EACH.

[math]b = \text {weight of bottom box}.[/math]
[math]t = \text {weight of stack}.[/math]
WRITE IN MATH NOTATION ALL QUANTITATIVE RELATIONS GIVEN IN ENGLISH

[math]t = w + w * \dfrac{1}{2} + \left ( w * \dfrac{1}{2} \right ) * \dfrac{1}{2} + \left \{ \left (w * \dfrac{1}{2} \right ) * \dfrac{1}{2} \right \} * \dfrac{1}{2}.[/math]
Can you simplify that using the distributive property?

Do you know what that kind of series is called?

Do you know a formula for calculating the sum no matter how many terms are involved?

 

[eddy2017]

Eddy

What is unknown? As the great Khan would say, what is the find?

ASSIGN A PRONUMERAL TO EACH.

[math]b = \text {weight of bottom box}.[/math]
[math]t = \text {weight of stack}.[/math]
WRITE IN MATH NOTATION ALL QUANTITATIVE RELATIONS GIVEN IN ENGLISH

[math]t = w + w * \dfrac{1}{2} + \left ( w * \dfrac{1}{2} \right ) * \dfrac{1}{2} + \left \{ \left (w * \dfrac{1}{2} \right ) * \dfrac{1}{2} \right \} * \dfrac{1}{2}.[/math]
Can you simplify that using the distributive property?

Do you know what that kind of series is called?

Do you know a formula for calculating the sum no matter how many terms are involved?

well, that is not a sequence, not a geometric series which involves a ratio, not a arithmetic series that involves a common difference.
it should then be a geometric series (which is the sum of all numbers in a geometric) sequence because I am doing a lot of multiplication here
let me have a try at distribution.

 

[eddy2017]

Eddy

What is unknown? As the great Khan would say, what is the find?

ASSIGN A PRONUMERAL TO EACH.

[math]b = \text {weight of bottom box}.[/math]
[math]t = \text {weight of stack}.[/math]
WRITE IN MATH NOTATION ALL QUANTITATIVE RELATIONS GIVEN IN ENGLISH

[math]t = w + w * \dfrac{1}{2} + \left ( w * \dfrac{1}{2} \right ) * \dfrac{1}{2} + \left \{ \left (w * \dfrac{1}{2} \right ) * \dfrac{1}{2} \right \} * \dfrac{1}{2}.[/math]
Can you simplify that using the distributive property?

Do you know what that kind of series is called?

Do you know a formula for calculating the sum no matter how many terms are involved?

One question. Should I simplify whatever is in brackets before i distribute?

 

[eddy2017]

i'm still working on this. please, do not post anything until i'm done

 

[eddy2017]

Look up geometric sequences. In particular, formulate for the nth term and the sum of n terms.

well, let's see, the n term is weight here,let's say the n term is w
the formula to find the nth term of a geometric series is
$<math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>a</mi><mi>n</mi></msup><mo>=</mo><msup><msub><mi>a</mi><mn>1</mn></msub><mrow><mi>n</mi><mo>-</mo><mn>1</mn></mrow></msup></math>$

 

[eddy2017]

to follow my first diagram and the sequence I am going to set this up like this


weight of the pile of boxes=10 + 5+ 2.5 + 1.25=18.75

b) Write and simplify an expression to find the weight of one stack of 4 boxes based on the unknown weight of the bottom box.
the formula for the geometric series is
an= (r^n-1)/(r-1) n term =? ratio = 0.5

Sorry for the tardiness. I am stuck here. don't know that the n term is,

 

[eddy2017]

Eddy

What is unknown? As the great Khan would say, what is the find?

ASSIGN A PRONUMERAL TO EACH.

[math]b = \text {weight of bottom box}.[/math]
[math]t = \text {weight of stack}.[/math]
WRITE IN MATH NOTATION ALL QUANTITATIVE RELATIONS GIVEN IN ENGLISH

[math]t = w + w * \dfrac{1}{2} + \left ( w * \dfrac{1}{2} \right ) * \dfrac{1}{2} + \left \{ \left (w * \dfrac{1}{2} \right ) * \dfrac{1}{2} \right \} * \dfrac{1}{2}.[/math]
Can you simplify that using the distributive property?

Do you know what that kind of series is called?

Do you know a formula for calculating the sum no matter how many terms are involved?

Eddy

What is unknown? As the great Khan would say, what is the find?

ASSIGN A PRONUMERAL TO EACH.

[math]b = \text {weight of bottom box}.[/math]
[math]t = \text {weight of stack}.[/math]
WRITE IN MATH NOTATION ALL QUANTITATIVE RELATIONS GIVEN IN ENGLISH

[math]t = w + w * \dfrac{1}{2} + \left ( w * \dfrac{1}{2} \right ) * \dfrac{1}{2} + \left \{ \left (w * \dfrac{1}{2} \right ) * \dfrac{1}{2} \right \} * \dfrac{1}{2}.[/math]
Can you simplify that using the distributive property?

Do you know what that kind of series is called?

Do you know a formula for calculating the sum no matter how many terms are involved?

Do you know a formula for calculating the sum no matter how many terms are involved
a sub1 times the common ratio raised to the n-1
an =a1 (r)^n-1

 

[Deleted member 4993]

to follow my first diagram and the sequence I am going to set this up like this


weight of the pile of boxes=10 + 5+ 2.5 + 1.25=18.75

b) Write and simplify an expression to find the weight of one stack of 4 boxes based on the unknown weight of the bottom box.
the formula for the geometric series is
an= (r^n-1)/(r-1) n term =? ratio = 0.5

Sorry for the tardiness. I am stuck here. don't know that the n term is,

Sum of weights of 4 boxes S = w + w/2 + w/4 + w/8 = w * (15/8)

Can you guess: What is 'w'?

 

[Deleted member 4993]

Do you know a formula for calculating the sum no matter how many terms are involved
a sub1 times the common ratio raised to the n-1
a_n =a₁ (r)^ (n-1) ......................................................................missing parentheses

That is NOT the sum ( even with the parentheses)

 

[eddy2017]

Sum of weights of 4 boxes S = w + w/2 + w/4 + w/8 = w * (15/8)

Can you guess: What is 'w'?

i am making no sense of that why /2 /4/ /8 ???

 

[Deleted member 4993]

i am making no sense of that why /2 /4/ /8 ???

Can you guess: What is 'w'?

Did you answer the question above?

If w = 10, what do you get from /2, /4, /8 ?

 

[eddy2017]

That is NOT the sum ( even with the parentheses)

how about,
an=a1 + n-1(d)

 

[Deleted member 4993]

how about,
an=a1 + n-1(d)

NO!!

You are pulling formulae randomly. Think a little bit.

 

[eddy2017]

there are 4 boxes, each one has a weight.
the sum of the boxes are:
S w1 + w2+ w3+w4
=18.75
We had settled that above. that is the total weight of the pile of boxes, right.
what to do next?

 

[Deleted member 4993]

We need to know how much each stack weighs in order to know how many stacks we can put on each pallet, but the bottom boxes do not necessarily weigh 10 pounds. In fact, we don’t know how much they weigh at all! Write and simplify an expression to find the weight of one stack of 4 boxes based on the unknown weight of the bottom box.

???? any help to reason this one out

Are you working on this problem?