Hello. I am in the sixth grade and I am new to this forum, my dad helped me sign up for when I have trouble with my work.
I Know that I have to make the express equal to the priority cost per pound but I don't know if the packaging material also gets reduced in cost also.
Below is problem #39 in my book. I have done all of them very well but I have trouble doing this one. Any help would be greatly appreciated.
---------------------------------
The cost of mailing a DVD in an envelope by Express Mail® is equal to the cost of mailing a DVD in a box by Priority Mail®. What is the weight of the DVD with its packing material? Round your answer to the nearest hundredth.
| Packing
Material | Priority
Mail | Express
Mail |
| Box | $2.25 | $2.50 per lb | $8.50 per lb |
| Envelope | $1.10 | $2.50 per lb | $8.50 per lb |
The exercise seems to me to be a bit cryptic. I'm going to
guess that the "Packing Material" costs are the costs for the materials, rather than the costs for mailing said materials. (This would be like if you went to, say, the UPS Store, and paid for the box, instead of just paying for the shipping of said box.)
So I
think we've got a situation where you have a fixed cost for each method of mailing, being the cost of the packaging, along with variable costs, being the cost of mailing the weight of the package plus its contents. (The contents could be just bubble-wrap of negligible weight, or could be rocks which are quite hefty; the weight of the box or the envelope itself would be the same.)
If I'm correct in my guesses as to what they're wanting you to assume, then let's call the weight of the DVD as "d", the envelope as "e", and the box as "b". This means that we have the following:
. . . . .Priority Mail: 2.25 + (d + b)*(2.5)
. . . . .Express Mail: 1.1 + (d + e)*(8.5)
This is a system of two expressions, which we can set equal to each other to create one equation. But it will be an equation in
three variables. This is a problem, because we cannot solve it algebraically. So... maybe they're asking for "the weight of the DVD with its packing material" because they're wanting us to consider only the cost of shipping the total weight, as one "item"...?
(I'm just guessing but, if one guess doesn't work, we try something else.)
So let's try setting it up that way: by considering only the cost of shipping the total weight. This time, "e" stands for the entire weight (DVD plus envelope and whatever is "Packing Materials") shipped by Express Mail, and "p" stands for the entire weight shipped by Priority Mail. Then we get:
. . . . .Priority Mail: 2.25 + 2.5*p
. . . . .Express Mail: 1.1 + 8.5*e
Now we're down to two variables, but these two expressions, when set equal, will still only create only one equation. This is still not solvable algebraically.
The fact that they're wanting you to "Round your answer to the nearest hundredth" suggests that there isn't a nice, simple solution. So we can't work our way backwards or fiddle around to get the answer. My guess is that (1) we're totally misunderstanding what they're meaning or (2) some information is missing. Sorry.
