Just so you guys know, I've already done like 20 questions... so it's not like you're DOING my homework for me... I just need help with two questions. We're supposed to solve these word problems through elimination or subsitution. #1. At a silversmith's shop, they have alloys that contain 40% silver and othets that are 50% silver. A custom order for a breacelet requires 150 grams of 44% silver. How much of each alloy should be melted together to make the bracelet? My two equations were: .4a + .5b = .44 a + b = 150 "a" means amount of 40% silver alloy "b" means amount of 50% silver alloy The answer in the back of the book is 90 g of 40% and 60 g of 50%, which sounds correct, but doesn't work when I subsititute it into my first equation, so I figure there's something wrong with my first equation. #2. During a training exercise, a submarine travles 16km/h on the surface, but it only goes 10 km/h underwater. If the submarine traveled a distance of 160 km in 12.5 hours, how long was it underwater. My equations were: 10a + 16b = 160km a + b = 12.5 hours So I changed the second equation to be b = 12.5 - a and then substituted that into the first equation to be: "a" refers to time spent underwater "b" refers to time spent above water 10a + 16(12.5 - a) = 160 10a + 200 - 16a = 160 -4a = 160 - 200 -4a = -40 -4a/-4 = -40/-4 a = 10 Then I subsituted the 10 into both equations: First Equation: 10(10) + 16b = 160 100 + 16b = 160 16b = 160 - 100 16b = 60 16b/16 = 60/16 b = 3.75 Second Equation: 10 + b = 12.5 b = 12.5 - 10 b = 2.5 So as you can see, it doesn't work out. If it helps, the answer in the back of the book is 6 hours and 40 minutes (for how long the submarine was underwater) I'll count myself lucky if anyone responds to this, so any help would be appreciated.. Thanks for helping out a confused grade 10. Andrew

Andrew, on #1 your first equation is forgetting that its 0.44 * c. Where c is the total weight. Try that and see how it works. I'll get to the second in a moment, I don't want to do to much for you to fast. Gotta keep you honest.

FWIW, I think you are making a similar mistake on #2. You have to keep your units consistent on both sides of the equation. In the first, you have a weight of silver and a purity rating on the left, but you only have a total weight on the right. So you aren't balancing the equation. Do you see what I'm getting at?

This is actually grade 10 math and Keith, I'll see if that helps... that is if I understand you correctly... Thnks for your time. Andrew

You got the answers in the back of the book? Hehehe...that reminds me what I would do. I would show all kinds of work and then at the end whatever I came out with if it didn't match the back of the book I would erase the final answer and just write in the back of the book answer. Most of the time the teacher didn't bother to check the work and just looked at the answer even though we were supposed to show all work.

You're absolutely correct for the first equation, Keith. I kept coing up with 66, and 44% of 150 is 66. It still amazes me the help you can get from this forum, even if it has nothing to do with Home Theater. Thanks agai, Andrew

Mike, Unfortunately all of my teachers' number one priority is the rough work. There's something like 3-5 marks for each question and if you just write the answer you get 1 mark. Really sucks for the easy questions that everyone can do in their heads because you still have to take up a quarter of the page with the rough work. Oh well. Andrew

Makes me think back to the days of calc in college. On some problems I'd start with a blank sheet of paper, do all my work on there until I got it right, then copy the stuff to the sheet I was handing in. Sometimes you might work only 3 or 4 problems on a single sheet. Do you see the relation between the two problems yet? They're fundamentally the same. In physics class they often require you to specify your units throughout the problem, which shows you how each side relates to the other. Remember that both sides of #2 are talking about km/h so you should be dealing with a formula where x+y=z and x,y,z are all km/h measurements.

Andrew - You setup the 2nd problem correctly, but you made an error in your math. Michael Perez is showing you the correction.

Well dammit, now I feel stupid. You just have an arithmetic mistake in #2, like Michael said. What I was referring too is that you're formula is really this: a * 10km/h + b * 16km/h = 160km Since a and b are units of time(h), your equation is balanced because you are multiplying a h value with a km/h value, thus cancelling the time. You can only add and subtract values that have the same unit. Does that make sense? I thought you didn't have all the units accounted for, like in the first problem, but you did. In your first problem you have: .4a + .5b = .44 or (a grams * .4p) + (b grams * 0.5p) = .44p where p is represent the unit for percantage of silver. So what you were doing was ending up with a formula that has different units on the different sides, so you couldn't work it. What you ended up with was: (a grams * .4p) + (b grams * 0.5p) = 150 grams * 0.44p a + b = 150 as your two equations which, as you found, can be solved. Clear as mud, eh?

Well I appreciate all the input from everybody. Turns out this was just busy work in the end, he didn't even collect it or refer to it at all... Oh well... it's practice for tests.. Thanks anyway, Andrew