Math Quiz for the Day

[Griff]

I went out to my reloading shop today and cast some bullets for my cowboy guns.  The ubiquitous 45 Colt... and for my long range guns, .30-30 & .32-40... (I already have plenty of .40 cal bullets for the Sharps.

So, I went thru 8 lbs of lead.  The .45s weigh as cast 237 grains, the .30 cals weight 150 grains and the .32s weigh in at 170.

How many bullets did I cast?

Oh yeah, none of y'all are mind readers, so I'll help a little:  For every 4 .45 bullets I cast, I cast 4 of the .30s and 3 of the .32s.

[AJMD429]

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Now THAT is the kind of math question we used to use for our homeschooled kids.

In fact, when my son was in 3rd grade and needed to learn multiplication tables 12 x 12, I wrote them out myself as fast as I could and then doubled that time and told him if he could write them out without errors thatfast I'd give him a handgun....

He still has that Ruger Mark-2 Pistol..

[Griff]

In high school I took a historical research course that was by "invitation only"... Only reason I got invited was that I'd had the teacher for Latin and US History previously. Good for college credit at the local State university. Semester long, with only product required was an outline of your proposed term paper for a mid term grade, and a final term paper meeting pretty strict parameters, no tests, quizzes, with full access to both our HS library, and the sponsoring University library. Had to have 20 students enrolled at the beginning of the semester. I think 9 of us survived. However, school district rules required a "final exam." Final exam consisted of 3 pages of history questions, no multiple choice, maybe 45 questions in total. 1 instruction: "Read all questions before beginning." I read all the questions... last question: "Print your name at the top of page one, sign here, turn exam in, & you're free to leave." A couple students didn't follow instructions...

[AJMD429]

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So...

237x4 + 150x4 + 170x3 means 948 + 600 + 510 or 2,058 grains per 'batch' and 8 x 7,000 grains to use up, or 56,000 grains.

56,000 / 2,058 is 27.21 so 27 batches would be 27x4 of the 45's and 30-30's, and 27x3 of the 32's, or 108 45's, 108 30-30's, and 81 of the 32's.

The "0.21" batch would either be wasteage or I suppose could result in a 'batch' of 2,058x0.21 or 432 grains, which could get you maybe one more 45 and one 32...

I'm gonna guess with some losses you got 100 of each of the 45's and 30-30's, and 80 of the 32's...???

[Griff]

Aw com'on, really? Doc is the only one to try... his answer is not correct... but also not wrong. I'll give y'all a hint: It can be expressed as 3 words, or 3 characters.

[earlmck]

Doc must have used the same algebra book I did 'cause we get the same "not correct" answer. ICU? No Griff, I don't CU I guess.

[Griff]

How many bullets did I cast?

Hint number 2: What question did I ask? *

* This might be the moment where you slap your forehead...

[jeepnik]

Well, assuming you ask the total number, using the amount of lead you stated you used the answer supplied is pretty darned close. Hard to be exact as there are things we don't know.

If you are asking how many "types" of bullets you cast the answer is three. But in that case the question is ambiguous.

[4t5]

108 , 108 , 81 .

[geobru]

299

237x+ 150x + .75(170x) = 56000
514.5x = 56000
x = 108.84

Rounding down to the nearest whole number since you can't have a partial bullet:
108+ 108 + 81 = 297

What happened to the extra lead?
108*237+108*150+.75(108)= 55566
56000-55566=434 grains that could be cast in an additional 2 bullets weighing 237 and 170 or 130

Assuming no wastage, and you utilized as much of the lead as possible while you were casting, you could get 299 bullets.
However, that would change the ratio of 4 4 3 that you gave us.
You can get 109 each of the 45 and 30 cal. .75*109=81.75. Round down to 81, the total number of bullets cast 109+109+81=299

[Griff]

Rounding down to the nearest whole number since you can't have a partial bullet:
108+ 108 + 81 = 297

Ding, ding, ding. Thank you. I didn't cull any of the bullets cast, and since the .45 & .30 caliber molds only produce an even number of bullets with each drop, (2 & 4 respectively), the .32 caliber is a 3-gang mold. Ergo, 297. So, in reality, I didn't quite consume 8 lbs of lead. But, that was the number of 1 lb ingots I added to the pot over the course of the day. I did have one short pour on the .30 cal mold, but all 4 went right back in the pot, and I re-poured that draw before proceeding with the rotation.

[jeepnik]

Solving a math problem without the necessary data is just a shot in the dark. Sort of like, solve for x. And the information you are given is y.