# Questions tagged [ratio]

For questions concerning the ratio of a certain quantity to another.

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### How to adjust a ratio to create desired proportion

Let's say I have a bunch of apples and oranges. Specifically 500 apples and 760 oranges. I need to create a big basket of fruit. For every 7 apples I include, I need to include 3 oranges. I want ...
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### What is the rigorous definition of the ratio of two numbers?

I have tried learning about ratios and proportions from a couple of books, but I have problems with the approaches they take. First of all, a definition is never actually given. Examples are given ...
326 views

### Find the value of p, q, r if $\frac{p}{q + r - p} = \frac{q}{p + r - q} = \frac{r}{p + q - r}$

I equated these 3 to k: $\frac{p}{q + r - p} = \frac{q}{p + r - q} = \frac{r}{p + q - r}$ = k and got k=1. After this, $\frac{p}{q + r - p} = k = 1$, and hence i got: $2p = q + r$ , $2q = p + r$ ...
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### At what angle must one cut the board?

Given a 2" wide board and a 1 1/2" wide board, we would like to cut the narrower board at an angle $\theta$ so the cut is 2" long so the boards will fit together as shown in the diagram below. At what ...
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### Showing this fraction is less than one?

And also, what are some techniques to show such a thing. That is, what are standard techniques for showing a fraction is less than one? I'm just trying to refresh/improve/add to my toolbox. The ...
2k views

### Is this a correct/good way to think interpret differentials for the beginning calculus student?

I was reading the answers to this question, and I came across the following answer which seems intuitive, but too good to be true: Typically, the $\frac{dy}{dx}$ notation is used to denote the ...
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### “Extending” the calculation of the golden ratio using square roots (not silver-ratio)

I'm looking at the following formula: $x =\frac{-n+\sqrt{n^{2}+4n}}{2}$ For $n=1$ this this gives $0.618...$ and then $\frac n x$ gives $1.618...$ which is $\phi$, the golden ratio. What ...
2k views

### Factors that Impact a Weighted Average the Most

I am trying to determine how to calculate the factors that have the most significant impact on a weighted average. For example, let's say I am reviewing the number of patients that responded to a ...
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### Ratios - Determining proportions/quantities

x : y = 8:5 Say I subtract a value of 400 from x and 300 from y, so that: ...
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### How to do this ratios problem without algebra?

Dinesh had some fiction and nonfiction books. The number of fiction was $4/9$ of the total number of books. After he had donated $80$ fiction books and $25$ nonfiction books, there were $20\%$ as many ...
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### Radius as a function of distance (ratios)

Seems like this is a simple question, but my own created equations don't seem to replicate results for other combinations of circles. Circle A at (0,0) has a radius of 6. Circle B at (15,0) has a ...
362 views

### “A project is normally finished in x days”, but this time new workers are coming in after y days. What should I base my solution on?

I am copying the following example from a textbook. Example: A project can be completed by 150 workers in 40 days. But the project manager brought in 30 more workers after 16 days. In how many ...
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### What is the difference between a simple “fraction” and a “common fraction”?

I have read about a common fraction in this statement (written in a text book): Ratio is the simplest form of a common fraction, in which the numerator denotes the antecedent and the denominator ...
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### Incomplete Question? - Ratio

I have encountered the following question in the famous "5LB book of GRE" book If the zoo currently has 80 total birds, what is the samllest number of birds that could be added such that atleast 20% ...
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### How is the Radius of Convergence of a Series determined?

Consider $$\sum_{n=0}^{\infty}\frac{(-1)^nx^n}{(n+1)^2}$$ which by the ratio test the ratio of two consecutive terms converges to $|x|$ as $n\rightarrow \infty$ and has a radius of convergence equal ...
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### Simple Ratio Question - What is wrong with my approach?

A zoo has twice as many zebras as lions and four times as many monkeys as zebras Their total is a multiple of ? (The answer is 11 but my solution gets me 13) Here is how I'm solving it: Z=2(L) -> [...
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### Proof of Menelaus using areas

I've tried to proof Menelaus' theorem using areas, but I've didn't figure out how. Some suggestions would be appreciated. Menelaus' Theorem states : Given a triangle ABC and a transversal ...
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### An Elementary Algebra (Ratios & Proportions) Problem

Let $a,b,c,d$ be positive real numbers in Continued Proportion (i.e., $\frac{a}{b} = \frac{b}{c} = \frac{c}{d}$), then show that $$d-a \ge 3(c-b).$$ or $$d -a = 3 + (some\ algebraic\ expression)$$
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### Error in ratio approximation

Not being very familiar with statistics I have been trying to figure this out for some time: Suppose that I am trying to determine the relative amounts of several animal species. To do this, I find ...
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