Questions tagged [ratio]

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

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2
votes
4answers
788 views

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 ...
2
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2answers
132 views

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 ...
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2answers
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: $2p = q + r$ , $2q = p + r$ ...
0
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1answer
479 views

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 ...
1
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1answer
38 views

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 ...
3
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3answers
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 ...
1
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1answer
99 views

“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 ...
0
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1answer
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 ...
0
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2answers
690 views

A cat chases a rat. For every $5$ leaps of the rat , the cat takes $3$ leaps

problem A cat chases a rat. For every $5$ leaps of the rat , the cat takes $3$ leaps, but the $2$ leaps of the cat are the same as $3$ leaps of the rat. Compare the speeds of the cat and the rat a)$...
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2answers
1k views

If $ \frac{y}{x-z} = \frac{x+y}{z} = \frac{x}{y} $ find the ratio of $x$, $y$ and $ z$

I have this question from higher algebra by Hall and Knight: if $ \frac{y}{x-z} = \frac{x+y}{z} = \frac{x}{y} $ then find the ratio of x,y and z? There are two answers given for this question, the ...
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1answer
3k views

Ratio of the areas of three concentric circles [closed]

A target is divided into three regions by concentric circles with radii that are in the ratio $1:2:3$ Find the ratio of the areas of the three regions in the form $a:b:c$ where $a$, $b$ and $c$ are ...
0
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2answers
1k views

Solving a Ratio Problem with Three Variables

A question that just popped in my head after reading an article: If the radius of Planet X is 16% larger than that of Earth, and Planet X has 40% the radius of Planet Y, then what is the radius of ...
1
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2answers
3k views

Writing a sentence as a proportion

I tried to write the following sentence as a proportion: 6 printers is to 24 computers as 2 printers is to 6 computers: ${6\,\,printers\over 2\,\,printers} = {24\,\,computers\over 6\,\,computers} $...
2
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1answer
2k views

Using ratio find the difference of two numbers will be [closed]

Two number are in the ratio 2:5 and become 4:7 when 5 is added to each of them.Twice the difference of two numbers will be.
2
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5answers
302 views

Understanding ratios in real world problems.

I'm studying maths as an adult, and I thought everything was going well until I hit the following activity. I have the answer in my workbook, but I just don't seem to be able to come to terms with the ...
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2answers
83 views

Solution dilutions

I don't need just the answer to this question I would like the formula on how to solve this question. I know that the final answer will be I need to add 15ml to make it a 10mg/ml titration but I do ...
2
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1answer
58 views

How to apply geometric series concepts into these numbers?

This is a basic level question and it is homework for someone that I am trying to help out. It is indicated as a Fibonacci puzzle. But I am not able to fit the numbers into a general geometric formula....
0
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2answers
26 views

Calculating percentages of two inputs

I'm pulling a blank on how to find how much of stream 1 to stream 2 is added to get stream 3 value I have two inputs (.60 and .20) with and out put of .50 I'm trying to remember the equation in ...
2
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2answers
509 views

Finding the fraction of a mixture using Ratio

This question is actually a GRE Question which comes under ratio topic and I have no clue on how to solve it Question Party Cranberry is ...
0
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1answer
125 views

Show that the ratio between two numbers is always proportional to the the maximum percentage error of their average?

The question is this: if we have a set of any random consecutive numbers, for example {1, 1.2, 4.2, 4.8, 5.6, 7.4, 9.8} then how can we prove that calculating the ratio between each of the numbers and ...
2
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1answer
52 views

The ratio of WHAT type of independent random variables is normal?

I know that the ratio of two independent normal random variables is a Cauchy random variable. The ratio of WHAT type of independent random variables is normal?
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3answers
63 views

Find the ratio of male teachers to male students

At a school function, the ratio of teachers to students is $5:18$. The ratio of female students to male students is $7:2$. If the ratio of the female teachers to female students is $1:7$, find the ...
1
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1answer
71 views

Find number of people given a set of ratios

I've been asked this question: A luna park with 3 attractions had its people buying tickets for the attractions in the following ratio: 6:5:12 in 2001. There have been 200 more people in 2002 and ...
2
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0answers
47 views

Mathematics of Poetry [closed]

Does anyone know of any sources that talk about (or know what topics I can start looking at that relate to) the mathematics behind poetry, e.g., ratios of syllables, equations for meter, frequency of ...
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1answer
79 views

Probability/Likelihood/Odds of Something Happening.

Here's my question/situation. Let's say there is a group of 100 people in a room and we are randomly picking one person in the group. Lets also assume that 10% of them are left handed. What's the ...
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1answer
33 views

acid/water/volume [closed]

I have a solution that is 50% acid and 50% water. I add 3 pints of pure acid to the solution and find that the solution is now 80% acid and 20% water. What is the volume of the original container.
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2answers
48 views

Find Ratio of Area of $ARPQ$ to Area of $ABC$

In $\Delta ABC$ $P$ ,$Q$ and $R$ are points on $BC$,$CA$ and $AB$ respectively such that $BP:PC=1:2$, $CQ:QA=3:2$ and $AR:RB=3:2$ Find $Ar(ARPQ):Ar(ABC)$ Any hint please
7
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7answers
619 views

What are the methods of dividing numbers to get weird values like $16\over 17$ without a calculator?

I tried estimating it to somewhere near $16\over 20$, but it's a far stretch from getting the actual $16\over 17$. How can one do so? Conventionally, I think for numbers such as $50\over 17$, or for ...
0
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3answers
826 views

what is the constant of proportionality?

I have been learning ratio and proportion lately and my teacher gave me this sum. If 7 oranges cost 700$, then how much will 60 oranges cost. She made a table which had 2 headings : Number of ...
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1answer
54 views

Ratios - Determining proportions/quantities

x : y = 8:5 Say I subtract a value of 400 from x and 300 from y, so that: ...
2
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0answers
73 views

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 ...
0
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1answer
35 views

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 ...
2
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2answers
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 ...
0
votes
1answer
393 views

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 ...
0
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2answers
61 views

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% ...
4
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2answers
108 views

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 ...
0
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2answers
602 views

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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0answers
215 views

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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2answers
93 views

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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1answer
34 views

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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0answers
63 views

Do all algebraic numbers have a sequence of integers where the ratio of consecutive terms tends to that number?

The most famous example of this is the Fibonacci sequence and the golden ratio. I feel like this should be obvious. But, if I have an algebraic number say: $\tan \left(\frac{15π}{16} \right) \...
1
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1answer
95 views

I Have 2 Different Ratios, How Do I Determine Which Has Better Odds?

I'm playing a game, and in the game you have the ability to trade your in game currency for opportunities at better players. I have 2 options: 5 Draws, each with a 2.5% chance of getting a really ...
1
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2answers
57 views

find the interval of convergence of the power series

like the title said i have to find the interval of convergence of this power series : $$\sum_{n=1}^\infty{ ((-1)^n *(x-1)^{2n-1})\over 3^n}$$ I applied the ratio test and i got something ...
0
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1answer
51 views

How do I determine the remaining ratio in this equation?

I'm developing an experience system for a game, where the experience is gained per hit. Anyways, I need to calculate how much EXP a user should get each time they hit a monster. So for example if a ...
0
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1answer
37 views

What is David's Salary per month?

John and David's salary adds upto 10,000 $ per month. They spend the same amount monthly and then it is found that ratio of their savings in 6:!. Which of the following is John's salary 6000 , 5000 , ...
1
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1answer
25 views

Show that the ratio of the distance $BD$ to $DC$ is $\gamma:\beta$

I'm struggling on the following question My approach to the question is as follows: The equation of line $BC$ is: $\lambda_1$b+$(1-\lambda_1)$c The equation of line $AP$ is: $\lambda_2(\beta$b$+\...
4
votes
2answers
277 views

What is the name for one side of a ratio?

Basic example: "If you are asked to put a ratio in the simplest form, make sure that you have found the smallest factor that goes into both [?]." I've tried searching for ratio diagrams in Google, ...
0
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1answer
66 views

Determine overall ratio from individual ratios

I have a set of statistics that I need to find the overall ratio to. This example will work with only two items so I'll write them down: ...
3
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1answer
69 views

How is $40$ related to $60$?

My problem with math is how I talk about it, the words of math. I know math is a language but I don’t translate it very well. For example, if you have $40$ units and I have $60$ units, from my ...
1
vote
1answer
747 views

Finding the smaller number of two given the ratio between sum, difference and product

How would you find the smaller of two numbers given the ratio between their sum, difference and product? I've been struggling with this one for a while. For example: the ratio between the sum, ...