Need to figure out a ratio for 3 different package sizes

hvanv

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Sep 19, 2007
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Hello - I have a production run of 453,000 grams of tea. I need to fill three types of containers: a loose can containing 141 grams; a loose pouch containing 453 grams; and a teabag can containing 120 grams.

Of the total amount of tea, 6% should go into the loose cans; 10% into loose pouches; and 84% into teabags.

What equation should I use to determine how many total grams of tea I need to set aside for all of the loose cans, loose pouches, and teabags?

Thank you,
H
 
hint ...

1% of the total 453000 g = 4530 g

so ... how much would 6%, 10%, and 84% of the total be?
 
If I just take 84%, 10%, and 6% of the total grams, that doesn't account for the different gram weights of the three packages - right?

And yes, the package is 141 grams, not 151 grams.

Am I missing some dead obvious way to figure this out? If I take the straight percentages that assumes that each type of package contains the same amount of grams - but they don't.

Still stuck...
 
For this problem

It does not matter

how much goes into each package.

In other words, those 141 gms, 453 gms and 120 gms are all superfluous information - you do not use those information for this part of the problem.
 
Just realized I've phrased the problem incorrectly...

Of the 453,000 total grams of tea, the number of units produced from that will be:

84% teabags, fill weight 120 grams
10% loose pouches, fill weight 453 grams
6% loose cans, fill weight 141 grams

So I can't just take 84% of the 453,000 grams to figure out how much tea to use for tea bags.

How do I account for the proper number of units of each type of packaging while also accounting for the diferent fill weights?

Thanks,
H
 
Re: Just realized I've phrased the problem incorrectly...

hvanv said:
Of the 453,000 total grams of tea, the number of units produced from that will be:

84% teabags, fill weight 120 grams
10% loose pouches, fill weight 453 grams
6% loose cans, fill weight 141 grams

So I can't just take 84% of the 453,000 grams to figure out how much tea to use for tea bags.

How do I account for the proper number of units of each type of packaging while also accounting for the diferent fill weights?

Thanks,
H
Now you will need those fill weights.

if you have 240 gms of tea for teabags - and each bag take 120 gmas of tea - how many bags of tea can you prepare?

Follow the same principle.

It will be useful if you show your work and indicate exactly where you are stuck - that way we know where do you need help.
 
Working on it...

Okay, so if I have 453,000 grams of tea I can make 3775 teabag cans of 120 grams per can.

Yesterday I tried taking 84% of that, which got me 380, 520 grams, and then trying to divide the balance of 72,480 grams between the loose cans and loose pouches. But at that point the numbers stopped making sense.

- H
 
Re: Working on it...

hvanv said:
Okay, so if I have 453,000 grams of tea I can make 3775 teabag cans of 120 grams per can.

Yesterday I tried taking 84% of that, which got me 380, 520 grams, and then trying to divide the balance of 72,480 grams between the loose cans and loose pouches. But at that point the numbers stopped making sense.

- H

Your answer for teabags is too high.

453000 * .84 = 380520

380520/120 = 3171

What about loose cans and loose pouches?
 
Is this the right starting point?

Do I really want to take 84% of the total amount of tea grams for teabags, when it is actually 84% of all units sold that are teabags? Does the amount of grams per teabag unit not matter for the first step?
 
Is this the solution?

If I take the 453,000 total grams and figure out what that could make of all three varieties, I get:

453,000 \ 120 = 3775 teabag cans * 84% = 3171 teabag cans

453,000 \ 141 = 3213 loose cans * 6% = 193 loose cans

453,000 \ 453 = 1000 pouches * 10% = 100 pouches

BUT - is this actually right???
 
No, that can't be right

Because it gives me a total number of loose cans that is higher than the total number of loose pouches, and only 6% of the units made should be loose cans versus 10% of units made that should be pouches.

So stuck again...
 
hvanv said:
Hello - I have a production run of 453,000 grams of tea. I need to fill three types of containers: a loose can containing 141 grams; a loose pouch containing 453 grams; and a teabag can containing 120 grams.

Of the total amount of tea, 6% should go into the loose cans; 10% into loose pouches; and 84% into teabags.

What equation should I use to determine how many total grams of tea I need to set aside for all of the loose cans, loose pouches, and teabags?

Thank you,
H
 
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