The cost of a square slab is proportional to thickness

[Borcho]

The cost of a square slab is proportional to thickness and also proportional to the square of its length. What is the cost of a square slab that is 3 m long and 0.1 m thick?

(1) The cost of a square slab that is 2 meters long and 0.2 meters thick is $160 more than the cost of a square slab that is 2 meters long and 0.1 meter thick
(2) The cost of a square slab that is 3 meters long and 0.1 meters thick is 300 more than the cost of a square slab that is 3 meters long and 0.1 meter thick

Answer is D.

I chose B... Confused. Does proportional imply a cost relationship at the same ratio as length or thickness? For example, a square slab of length L costs kL, hence the ratio of cost between two slabs of lengths La = 2 and Lb =3 is 2:3? Could someone help me with the formula translation. Thanks.

[Harish Dorai]

The description of how cost is proportionate to length and thickness can be converted to an equation as follows:

Cost = k x Square(Length) x Thickness, where k is a constant.

We are now asked to find the cost, for a slab of given length and thickness. In order to find the cost, we need to determine the constant "k".

Statement (1): The cost of a square slab that is 2 meters long and 0.2 meters thick is $160 more than the cost of a square slab that is 2 meters long and 0.1 meter thick

So that means k x Square(2) x 0.2 = k x Square(2) x 0.2 + $160
From the above equation you can determine "k". So we can plug this in the equation to find the cost of the 3 meter long slab. HENCE SUFFICIENT.

Statement (2): The cost of a square slab that is 3 meters long and 0.1 meters thick is 300 more than the cost of a square slab that is 3 meters long and 0.1 meter thick. The above statement is very similar to Statement (1), except for the difference in dimensions and costs. So this statement is also SUFFICIENT to determine the cost.

Hence answer is (D).

[Borcho]

I am not sure why you square the length. I don't think this is correct.

[Borcho]

Ignore my previous comment. I know reread the question. Thanks.

[Luci]

Sorry but is statement 2 correct?

(2) The cost of a square slab that is 3 meters long and 0.1 meters thick is 300 more than the cost of a square slab that is 3 meters long and 0.1 meter thick

how a slab that is identical is going to be 300$ more? The lenght and the thickness is the same for both slabs, isn´t it?

I guess I´m missing something

Thanks

[esledge]

Harish, well done on the explanation.

Luci, that has to be a typo in (2), but it threw me off, too.

Borcho, can you please clarify the dimensions given in (2) for future forum users?

Thanks all!

[Borcho]

The cost of a square slab is proportional to thickness and also proportional to the square of its length. What is the cost of a square slab that is 3 m long and 0.1 m thick?

(1) The cost of a square slab that is 2 meters long and 0.2 meters thick is $160 more than the cost of a square slab that is 2 meters long and 0.1 meter thick
(2) The cost of a square slab that is 2 meters long and 0.1 meters thick is 300 more than the cost of a square slab that is 3 meters long and 0.1 meter thick

Answer is D.

[BG]

Based on "The cost of a square slab is proportional to thickness and also proportional to the square of its length"
I figured Cost=k x Square(Length) , Cost=m x Thickness

Then Cost(2)=k x m x Squre(Length) x Thickness

Under Dorai's formula, Cost = k x Square(Length) x Thickness, which means "The cost of a square slab is proportional to the product of thickness and the square of its length. it is not consistent with the original info, or this is another way to express the same meaning as the original info.

Really need help

[Saurav]

Under Dorai's formula, Cost = k x Square(Length) x Thickness, which means "The cost of a square slab is proportional to the product of thickness and the square of its length.

this is another way to express the same meaning as the original info.

Based on "The cost of a square slab is proportional to thickness and also proportional to the square of its length"
I figured Cost=k x Square(Length) , Cost=m x Thickness

This is incorrect since, if you write Cost=k x Square(Length), then you are saying the that cost depends only on the length and nothing other than that (Cost cannot be equal to m x Thickness). Similarly Cost=m x Thickness means Cost depends only on thickness.

Then Cost(2)=k x m x Squre(Length) x Thickness should be correctly written as (Dorai's formula) Cost = k x Square(Length) x Thickness

I hope the (2) above means raised to power 2, also, k x m ---> a constant x another constant which you can also write as n (a third constant without much ado)

[BG]

appreciate

[RonPurewal]

Under Dorai's formula, Cost = k x Square(Length) x Thickness, which means "The cost of a square slab is proportional to the product of thickness and the square of its length.

this is another way to express the same meaning as the original info.

Based on "The cost of a square slab is proportional to thickness and also proportional to the square of its length"
I figured Cost=k x Square(Length) , Cost=m x Thickness

This is incorrect since, if you write Cost=k x Square(Length), then you are saying the that cost depends only on the length and nothing other than that (Cost cannot be equal to m x Thickness). Similarly Cost=m x Thickness means Cost depends only on thickness.

Then Cost(2)=k x m x Squre(Length) x Thickness should be correctly written as (Dorai's formula) Cost = k x Square(Length) x Thickness

I hope the (2) above means raised to power 2, also, k x m ---> a constant x another constant which you can also write as n (a third constant without much ado)

extremely well explained.

[davetzulin]

sorry to bump such an old thread. what is trivial to the people who responded is apparently non-trivial to me.

if the problem states that cost is proportional to area and cost is proportional to thickness, what was the conceptual thinking that allows one to multiple both and then make them proportional such that cost = k * area * thickness.

**the whole time i figured this was a cost per volume, but I did not want to bring outside info.

Is my algebra correct?

c = A * q (area and constant k)
c = T * k (thickness and constant q)

A = c/k
T = c/q

A*T = c^2 / (k*q)

isolate c

c = A*T * (k*q/c)

so the solution originally posted just turns the expression in the parenthesis into its own new constant.

[tim]

while not mathematically rigorous, if that approach helps you understand the problem, go with it! basically to be proportional to area means it's the area times *something*; same deal with thickness. let us know if you have any further questions on this one..

[priyankadhawan223]

hi

sorry, for this LATE!!

is it possible to look at this question in another way:

1) this statement basically says that 0.1m costs $160. therefore, 3m and 0.1m would cost us 31*160?

2)similarly, this statment says, 1m costs $200. we convert 1m to equal 0.1 parts and add the 0.1 part to 3(200)

thanks

[tim]

no, you don't want to look at either statement as saying that there is a certain cost per meter. this is completely different from what the problem is describing. that kind of a shortcut can get you into serious trouble on problems of this type..