estimate

eddy2017

eddy2017

Elite Member
Joined
Oct 27, 2017
Messages
2,525
Hi, dear teachers:
I am still having doubts when I need to set up a proportion. in the following problem I can I can set up a proportion to solve it.
I am asking advice on how to know for sure how to go about setting it up, like, if there is a definite rule for it.
Here's the problem and my solution.
To estimate the population of grasshoppers in a field, a biologist counts 60 grasshoppers in a randomly selected 4 ft^2 section of the field. Which of the following is the best estimate for the total number of grasshoppers in the field if it measures 200 square feet?.
choices
2500
2400
3000
4000

`I will set up a proportion
'60 grasshoppers = 200 ft^2
4feet^2...........................x grasshoppers`

Is this the correct way to set up the proportion.
The final result of the operation is 3000, but what i want you to confirm if the units in the proportion are set up right.
Thanking you in advance for any hints or help,
eddy
 
Last edited:
eddy2017 said:
Hi, dear teachers:
I am still having doubts when I need to set up a proportion. in the following problem I can I can set up a proportion to solve it.
I am asking advice on how to know for sure how to go about setting it up, like, if there is a definite rule for it.
Here's the problem and my solution.
To estimate the population of grasshoppers in a field, a biologist counts 60 grasshoppers in a randomly selected 4 ft^2 section of the field. Which of the following is the best estimate for the total number of grasshoppers in the field if it measures 200 square feet?.
choices
2500
2400
3000
4000

`I will set up a proportion
'60 grasshoppers = 200 ft^2
4feet^2...........................x grasshoppers`

Is this the correct way to set up the proportion. ...................................................NO!
The final result of the operation is 3000, but what i want you to confirm if the units in the proportion are set up right.
Thanking you in advance for any hints or help,
eddy
Click to expand...
you ask:

Is this the correct way to set up the proportion. ...................................................NO!​

The left-hand-side of the equation has dimension of (grasshoppers/ft2)

The Right-hand-side of the equation has dimension of (ft2/grasshoppers)

Those two are not equal!

By the way, you did not define 'x'!
 
eddy2017 said:
Hi, dear teachers:
I am still having doubts when I need to set up a proportion. in the following problem I can I can set up a proportion to solve it.
I am asking advice on how to know for sure how to go about setting it up, like, if there is a definite rule for it.
Here's the problem and my solution.
To estimate the population of grasshoppers in a field, a biologist counts 60 grasshoppers in a randomly selected 4 ft^2 section of the field. Which of the following is the best estimate for the total number of grasshoppers in the field if it measures 200 square feet?.
choices
2500
2400
3000
4000

`I will set up a proportion
'60 grasshoppers = 200 ft^2
4feet^2...........................x grasshoppers`

Is this the correct way to set up the proportion.
The final result of the operation is 3000, but what i want you to confirm if the units in the proportion are set up right.
Thanking you in advance for any hints or help,
eddy
Click to expand...
It makes sense to use a proportion. It's assumed that grasshoppers are uniformly distributed, so the amount of grasshoppers is proportional to the area.
Your proportion is incorrect, please double check.
 
Thanks a lot. That was the tip I needed. I did not how to set it up. So, it should be, then, like this:

`60 grasshoppers = 4ft^2
x grasshoppers 200 ft^2 [Units have to line up vertically. I was in doubt about that].

x = 60 gh * 4 ft^2
200 ft^2
x= 3000 grasshoppers.` ( This is the best estimate)
 
eddy2017 said:
Thanks a lot. That was the tip I needed. I did not how to set it up. So, it should be, then, like this:

`60 grasshoppers = 4ft^2
x grasshoppers 200 ft^2 [Units have to line up vertically. I was in doubt about that].

x = 60 gh * 4 ft^2
200 ft^2
x= 3000 grasshoppers.` ( This is the best estimate)
Click to expand...
Your proportion "part" is okay (still no definition of 'x').

However, next line is NOT correct.
 
eddy2017 said:
Thanks a lot. That was the tip I needed. I did not how to set it up. So, it should be, then, like this:

`60 grasshoppers = 4ft^2
x grasshoppers 200 ft^2 [Units have to line up vertically. I was in doubt about that].

x = 60 gh * 4 ft^2
200 ft^2
x= 3000 grasshoppers.` ( This is the best estimate)
Click to expand...
No, "Units have to line up vertically" is not correct.
Here's an example: 1 cup of lemon juice makes 8 cups of lemonade. How much lemon juice you need for 16 cups of lemonade?
As you can see all units are cups. How do you line them up?
 
eddy2017 said:
Hi, dear teachers:
I am still having doubts when I need to set up a proportion. in the following problem I can I can set up a proportion to solve it.
I am asking advice on how to know for sure how to go about setting it up, like, if there is a definite rule for it.
Here's the problem and my solution.
To estimate the population of grasshoppers in a field, a biologist counts 60 grasshoppers in a randomly selected 4 ft^2 section of the field. Which of the following is the best estimate for the total number of grasshoppers in the field if it measures 200 square feet?.
choices
2500
2400
3000
4000

`I will set up a proportion
'60 grasshoppers = 200 ft^2
4feet^2...........................x grasshoppers`

Is this the correct way to set up the proportion.
The final result of the operation is 3000, but what i want you to confirm if the units in the proportion are set up right.
Thanking you in advance for any hints or help,
eddy
Click to expand...
Are the units correct? Just look at them! Does gh/ft^2 = ft^2/gh? Are both sides exactly the same? If yes, then your work is fine if not then your work is not fine. It is just a matter of looking!

I asked before and I will ask again: How do you get the correct answer even though your equation is wrong? Do you have the solution from your textbook or something like that?
 
lev888 said:
No, "Units have to line up vertically" is not correct.
Here's an example: 1 cup of lemon juice makes 8 cups of lemonade. How much lemon juice you need for 16 cups of lemonade?
As you can see all units are cups. How do you line them up?
Click to expand...
Thanks,
Maybe this way is less confusing for me.
If it can be done this way,
1 cup of lemon juice = 8 cups of lemonade
x cups lemon juice needed = 16 cups
8x =1*16
x= 16
x=2
2 cups of lemon juice are needed to make 16 cups of lemonade.
 
It might be better to just think about the problem rather then jumping to formulas/proportion.
You are told that there are 60 grasshoppers in a randomly selected 4 ft^2 section of the field. This means that you are going to assume that every 4ft^2 has approximately 60 grasshopper. How many 4ft^2 are there in 200 ft^2. Answer is 50. So you have 50 4ft^2 areas that each have approximately 60 grasshopper. So there will be approximately 50*60 grasshoppers in a 200 ft^2 area.
 
Last edited:
Jomo said:
Are the units correct? Just look at them! Does gh/ft^2 = ft^2/gh? Are both sides exactly the same? If yes, then your work is fine if not then your work is not fine. It is just a matter of looking!

I asked before and I will ask again: How do you get the correct answer even though your equation is wrong? Do you have the solution from your textbook or something like that?
Click to expand...
No, I did not. I just performed the operation that was there in plain sight. I think this is the type of problem you can get it right ( the amount, that is) even when you do not follow the steps as it is.
 
eddy2017 said:
Thanks,
Maybe this way is less confusing for me.
If it can be done this way,
1 cup of lemon juice = 8 cups of lemonade
x cups lemon juice needed = 16 cups
8x =1*16
x= 16
x=2
2 cups of lemon juice are needed to make 16 cups of lemonade.
Click to expand...
Why do you have x=16 and x=2? Does 2=16? Your equal signs must ALL be valid.
 
eddy2017 said:
No, I did not. I just performed the operation that was there in plain sight. I think this is the type of problem you can get it right ( the amount, that is) even when you do not follow the steps as it is.
Click to expand...
Nonsense! Wrong equations yield wrong answers.
 
Jomo said:
It might be better to just think about the problem rather then jumping to formulas/proportion.
You are told that there are 60 grasshoppers in a randomly selected 4 ft^2 section of the field. This means that you are going to assume that every 4ft^2 has approximately 60 grasshopper. How many 4ft^2 are there in 200 ft^2. Answer is 50. So you have 50 4ft^2 areas that each have approximately 60 grasshopper. So there will be approximately 50*50 grasshoppers in a 200 ft^2 area.
Click to expand...
every 4ft^2 has approximately 60 grasshopper.
50 ft^2 in 200 ft^2
fifty 4 ft^2 areas have approximately 60 grasshoppers each.
50 * 60 =3000
I like that.
 
eddy2017 said:
Thanks,
Maybe this way is less confusing for me.
If it can be done this way,
1 cup of lemon juice = 8 cups of lemonade
x cups lemon juice needed = 16 cups
8x =1*16
x= 16
x=2
2 cups of lemon juice are needed to make 16 cups of lemonade.
Click to expand...
Do you think this is a better way to set it up instead of going for the fraction type of thing?.
 
Jomo said:
Are the units correct? Just look at them! Does gh/ft^2 = ft^2/gh? Are both sides exactly the same? If yes, then your work is fine if not then your work is not fine. It is just a matter of looking!

I asked before and I will ask again: How do you get the correct answer even though your equation is wrong? Do you have the solution from your textbook or something like that?
Click to expand...
So,
Jomo said:
Nonsense! Wrong equations yield wrong answers.
Click to expand...
Let me set it up again.
60 grasshoppers= 4ft²
X gh= 200ft²
4x=60 gh * 200ft²
I will divide 4 into both sides
X= 60 gh * 200 ft²/4ft²
X= 300 grasshoppers [ ft² cancels out]
 
eddy2017 said:
Do you think this is a better way to set it up instead of going for the fraction type of thing?.
Click to expand...
I didn't say fractions is the wrong way. I said lining up units is the wrong way. Sure, when units are different this method of checking works. But you should understand _why_ it works.
What does it mean a is proportional to b? It means a=kb, where k is a constant.
So, 1 cup lemon juice is proportional to 8 cups of lemonade => 1 cup of LJ = k * 8 cups of L => k = 1/8
x cups of lemon juice is proportional to 16 cups of lemonade => x = k * 16 => k = x/16
Therefore, 1/8 = x/16 - these are your fractions.

As a shortcut you can write it down in plain English, but in _LOGICAL_ manner:
1 cup lemon juice makes 8 cups of lemonade
x cups lemon juice makes 16 cups of lemonade
This results in proportion 1/8 = x/16

You don't write
1 cup lemon juice makes 8 cups of lemonade
16 cups of lemonade makes x cups lemon juice
which would result in an incorrect proportion 1/8 = 16/x

See the difference? If you checked units you would not have caught this error.
 
You must log in or register to reply here.
Top