How to solve problems that use a number of items per a set, then extrapolate that to a larger set.

Question

OKay, I know this is a homework question, but I am the dad and I really need to know the proceedure for this!

Here's the question:

One out of every 62.4 batteries is defective. If a company makes 374,400 batteries a day, how many are defective?

I'd like to have the process to get the answer too. Meaning I want to know the steps to solve the problem.

If it were 1 in 100, could you do it? What process would you use then? What if you had 1 in 5 out of 20? What would you do? That is, are there any simpler problems you could do? Give us more insight on what makes this problem difficult for you. — Milo Brandt, Sep 06 '16 at 23:30
Well, not having a mind for math! But, it was the percentage per day, I kept thinking I had to know what percent 1 was of 62.4 — user3687778, Sep 06 '16 at 23:35
Just a side note, if you are a kid who needs homework help, just own up to it. If not, just disregard this. — suomynonA, Sep 06 '16 at 23:39
Uhm no, I am the Dad, for real. I didn't know the process for this question. I needed help and I got it. Thanks for checking though. — user3687778, Sep 07 '16 at 14:57

Brian Tung · Accepted Answer · 2016-09-06T23:34:30.863

2

Divide $374400$ by $62.4$. That's literally all there is to it, on average.

Slight elaboration: You're given a number of batteries per day. You're also given a defect rate in batteries per defect. If you divide the former by the latter, you'll get defects per day. We can see this more viscerally, perhaps, in the units conversion:

$$ \frac{374400 \text{ batteries}}{\text{day}} \div \frac{62.4 \text{ batteries}}{1 \text{ defect}} = \frac{N \text{ defects}}{\text{day}} $$

Your desired answer is $N$.

If there were some other number $k$ defects per $62.4$, you would write

$$ \frac{374400 \text{ batteries}}{\text{day}} \div \frac{62.4 \text{ batteries}}{k \text{ defects}} = \frac{N \text{ defects}}{\text{day}} $$

so you'd have to divide $62.4$ by $k$ to get the number of batteries per single defect, and then divide $374400$ by that first result to get your final answer. That turns out to be the same as dividing $374400$ by $62.4$ (as we did previously when $k = 1$), and then multiplying it by $k$. Try it!

edited Sep 06 '16 at 23:34

answered Sep 06 '16 at 23:28

Brian Tung

34,160

What if it were 2 or 3 batteries out of 62? Would you try to simplify that? – user3687778 Sep 06 '16 at 23:31
@user3687778: I have edited my answer. Did you downvote, or was that someone else? – Brian Tung Sep 06 '16 at 23:34
Someone else, this is a great answer! – user3687778 Sep 06 '16 at 23:35
This account isn't linked to my stackoverflow one, I need to fix that. – user3687778 Sep 06 '16 at 23:36
@user3687778: OK. Well, it happens. – Brian Tung Sep 06 '16 at 23:40
@EthanBolker: It's possible that someone doesn't like to see trivial questions answered. But that's just speculation on my part. – Brian Tung Sep 06 '16 at 23:41
@BrianTung Perhaps. In my view this isn't just an answer to a trivial question.The OP has asked for a process, and this answer provides one. Hence my upvote. – Ethan Bolker Sep 06 '16 at 23:49
@EthanBolker: Thanks for the kind words! – Brian Tung Sep 06 '16 at 23:50
As the OP, I agree, this is exactly what I wanted. I had to explain this to my 11 year old and honestly I didn't know the process. I got what I needed to understand the problem in the way my 40 year old mind works. I helped him, he got the problem right. That's success. – user3687778 Sep 07 '16 at 14:57

score 2 · Answer 2 · answered Sep 06 '16 at 23:39

You can solve this with simple multiplication. Since one out of $62.4$ batteries is defective, the fraction representing the number of defective batteries is $\frac1{62.4}$. You multiply this by the total number of batteries, which gets you the following equation:

$$ \frac1{62.4} * 374,400=x$$

$$\frac{374,400}{62.4}=x$$

$$6000=x$$$x$ is the total number of batteries.

How to solve problems that use a number of items per a set, then extrapolate that to a larger set.

2 Answers2