Yahoo Answers is shutting down on May 4th, 2021 (Eastern Time) and beginning April 20th, 2021 (Eastern Time) the Yahoo Answers website will be in read-only mode. There will be no changes to other Yahoo properties or services, or your Yahoo account. You can find more information about the Yahoo Answers shutdown and how to download your data on this help page.
Trending News
![[GIANNI]'s avatar](https://s.yimg.com/dh/ap/social/profile/profile_b48.png)
helpme with algebra problem?
suppose that cool tech corporation makes wigets, gidgets and sprockets. while all 3 items get the same indivisual packing, they all witgh different amounts. including the packaging, they all wigh different amounts. including thr packaging. widgets weigh 3 ounces. gigets are 4 ounces and sprockets are 5 ounces. the shipping box used can only hold 30 packaged items, and they will have to pay extra shipping if the total weight is above 96 ounces.
1. how many ways can shipping boxes be filled that will make use of the full 96 ounces and full 30 items that they can fit without going over 96 ounes
2. list all possible ways to pack the boxes if you guarentee that each store will get atleast 1 of all 3 parts
thanks
1 Answer
- ?Lv 78 years ago
1. The lightest possible box with 30 items in it would be a box of 30 widgets (90 ounces).
So replacing widgets with gidgets or sprockets, we're only allowed to add 6 ounces,
at 1 oz per gidget and 2 per sprocket. This makes the question equivalent to asking how many ways we can write 6 as a sum of 1s and 2s, and the answer is
4 ways, depending on whether we use zero, one, two, or three 2s.
2. Of the 4 ways we calculated in part 1,
one of them (six 1s) would describe a box with no gidgets
and one of them (three 2s) would describe a box with no sprockets.
So there are only 2 possible ways to pack the boxes if all three parts are included:
25 widgets, 4 gidgets, and 1 sprocket; or
26 widgets, 2 gidgets, and 2 sprockets.