Word Problems & Functional Models

B

Becky4paws

Junior Member
Joined
Feb 15, 2006
Messages
63
The sum of two numbers is 18. Express the product of the numbers as a functions of the smaller number.

18 = x+y
18-x = y

xy = 18
x(18-x) = F(x)

These type of problems intimadate me. How do you know if I am setting these problems up right? The way you are instructed to express your answer as a function of it's length, or as a function of the smaller number, I am unsure if I understand this at all.

A closed box with a square base is to have a volume of 1,500 cubic inches. Express its surface ara as a function of the length of its base.

Volume = (length x)(width y)(height z)
1,500 = xyz
1,500/yz = x

F(x) = 1,500 = (1,500/yz)(w)(h)

That doesn't feel right.
 
You did fine with the first one.
The second one you ignored or mis-read parts of the question. Ya gotta read carefully.
"closed box with a square base"
"Express its surface area"

Things will work better if you choose variable names that tie in to the problem (or if you insist, at least define what x is.)
The smaller number is s.
The length is l.

The side of the base is b.
The height is h.
The base is square so there are only two variables.
V=b^2*h
SA = 2b^2+4bh
Try it again with those equations.
 
Becky4paws said:
The sum of two numbers is 18. Express the product of the numbers as a functions of the smaller number.

18 = x+y
18-x = y

xy = 18
x(18-x) = F(x)

These type of problems intimadate me. How do you know if I am setting these problems up right? The way you are instructed to express your answer as a function of it's length, or as a function of the smaller number, I am unsure if I understand this at all.

A closed box with a square base is to have a volume of 1,500 cubic inches. Express its surface ara as a function of the length of its base.

Volume = (length x)(width y)(height z)
1,500 = xyz
1,500/yz = x

F(x) = 1,500 = (1,500/yz)(w)(h)

That doesn't feel right.
Click to expand...

Hi!

One of our illustrious volunteers here often starts out his answers by saying "NAME things."

If you name what your variables stand for, then you will eliminate all of the uncertainty you have expressed in your question.

In the example you have posted, suppose you NAME things this way:
Let x = the smaller number

The problem states that the sum of the two numbers is 18, so the LARGER number would be 18 - x.

Now, the product of the two numbers is smaller * larger, or
Product = x(18 - x)
Product = 18x - x^2

Is the product expressed in terms of the smaller number, x? I think so.

I hope this helps you.
 
Double check me please

On the second equation, a closed box with a square base, you gave me the equations: V=b^2*h and SA=2b^2+4bh. I understand that I am to solve one equation by eliminating one of the variables, but I'm not always sure which equation I should solve and which equation I should substitue the answer into. In the case of the previous problem, I assume I would solve 1,500=b^2*h by eliminating one of the variables and then substitue that answer into the SA equation. But how do I know which varible to solve for - b^2 or h - and why?
 
For most problems it doesn't matter which you choose to start with 'cause you are looking for all the variable values. In this one you want to "Express its surface area as a function of the length of its base" which is b so you don't want to eliminate b. You are looking for SA so you want to end up with that. Solve the volume equation for h. Replace h in the SA equation with that and you are done.
--------------------
Gene

PS. I hope you see where the equations came from.
 
Double check

I understand where the equations came from and hope this is how it should work out.

V=b^2(h)
1500 = b^2(h)
1500/b^2 = h

substituting:

SA =2b^2 +4bh
SA =2b^2 +4b(1500/b^2)
 
You must log in or register to reply here.
Top