Questions tagged [ratio]

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

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Dividing Numbers Into Rations

The question is: Suppose $60$ is divided into $3$ parts in the ratio of $1$:$3$:$6$. What is the value of the middle part? I tried to take $60$, divide it into $3$ parts and divide those $3$ parts ...
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4k views

How to calculate a distance with different fraction ratios?

This is the math question for my sixth grader son. The answer is $136$ meters but could not figure it out. Can someone please explain how to solve it. Thank you. Adam first walks $3/8$th of a road. ...
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2answers
342 views

Ratios with Ages

The ratio of Sam's age to his son John's age is 8:3. If the sum of their ages is 55 years, what is the age difference between John and his dad in years? So, I divided 55 by 11 and got 5, then ...
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384 views

Given that $yz:zx:xy = 1:2:3$ and $\tfrac{x}{yz}: \tfrac{y}{zx} = 1:k$, find $k$

Given that $yz:zx:xy = 1:2:3$ and $\dfrac{x}{yz}: \dfrac{y}{zx} = 1:k.$ Find $k$. I understand that $ k = \frac{y^2}{x^2}, y = 1,$ and $x = 2$. Therefore $k = \frac{1}{4}$. This also brings me to $z ...
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How to calculate a performance ratio when your goal is zero?

When it comes to performance ratio the standard answer is quite simple. Let's say for example we have a car manufacturer who aims to manufacture $1000$ cars and he just made $900$ so have here $\frac{...
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1answer
85 views

Ratio of squares touching edge of circle?

Consider an infinite amount of squares stacked on top of each other where the top left corners are touching the edge of a circle: Call the largest blue square x. How would I find the ratio of square ...
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1answer
54 views

Convergence of $\sum_{n=0}^{\infty} \frac{3^{2n}}{(2n)!}$

I need help determining what following series converges to using the ratio test. $$\sum_{n=0}^{\infty} \frac{3^{2n}}{(2n)!}$$ It's the end that really has me confused with what to do with the ...
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2answers
654 views

Ratio of sines given, find ratio of cosines?

Is it possible to find $\displaystyle{\cos x \over \cos y}$ if $\displaystyle{\sin x\over \sin y}$ is given? If so, how would one approach this problem? Thank you in advance!
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1answer
2k views

How do you do this *without* using a calculator? The ratio of three numbers is $3\frac{1}{3}:4\frac{1}{5}:6\frac{1}{8}$

The ratio between three numbers is: Three and one third: Four and one fifth: Six and one eighth and the sum of the numbers is $4197$. What are the three numbers? Using a calculator, I would just add ...
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3answers
4k views

Ratio between two numbers is 6:7 and the difference between them is 10. What are the two numbers?

I know the numbers are $60$ and $70$ but I got that by trial and error. Is there some other more logical way to do this problem?
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2answers
766 views

Find common ratio of a geometric sequence given the sum

I feel like I have tried everything with this problem. Here it is: Since this is an infinite sequence, I believe the formula for the sum is found with the equation firstTerm/(1-ratio). I get 6x^7 ...
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1answer
35 views

Related rates question.

Two sides of a triangle have lengths $\sqrt{21}~m$ and $\sqrt{7}~m$. The angle between them is increasing at a rate of $\dfrac{2}{\sqrt{3}}~rad/sec$. How fast is the altitude of the triangle ...
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58 views

maximization of a particular ratio

We are given a ratio: $$\frac{g(x)}{f(x)}$$ where: $$g(x) \in \mathbb{R}^{+}$$ $$f(x) \in \mathbb{N}\: \cap f(x)\ge 2$$ So $g(x)$ returns values in $[0,+\infty]$ while $f(x)$ returns values in $...
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34 views

ratio based question

If p,q and r are three distinct real numbers such that $(pq+1):(qr+1):(rp+1)$ is $q:r:p$,then prove that $|pqr|=1$.
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193 views

Can $\pi$ be a ratio of angles?

I know that $\pi$ is the ratio between various measurements in 2 and 3 dimensional shapes. (For example, $V=\pi r^2h$ for a right circular cylinder can be written as $\pi=\frac{V}{r^2h}$) The golden ...
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1answer
49 views

Prove that if a fraction is broken up into two the resulting two fractions cannot both have a larger value [duplicate]

I am working on research involving probability tables. I simplified the problem to the following. Say we have the following: $C_1, C_2, C_3, C_4$ $\forall i, C_i > 0$ $x = \frac{C_1 + C_2}{C_1 + ...
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497 views

Ratio of downstream and upstream velocity

A boat first travels downstream for $21$ km then it turns the opposite direction and travels upstream for $4$ km. It repeats again but now it travels downstream for $12$ km then travels upstream for $...
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1answer
113 views

Simple travelling ratio problem? Do we need to first find the distance?

A car and a truck start off from Town A and Town B respectively and travel towards each other. The ratio of the speed of the car and the truck is 2 : 3. If it takes 5.5 hours for the car to travel ...
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2answers
145 views

Can ratios really be manipulated as fractions?

In high-school Maths, we were taught that it was possible to manipulate ratios as fractions. For example, $$ 1 : 7 = 3 : x \\ \frac{1}{7} = \frac{3}{x} \\ \frac{x}{7} = 3\\ x = 3 \times 7\\ x = 21\\ $$...
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338 views

An Impossible Ratio

I'm facing a bit of a difficulty thinking about the aspect ratio of A4 paper. The beauty of this paper size is that when it is folded in half along the longer side, it becomes A5 paper which has ...
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1answer
10 views

query on shares

A person bought a share (par value is rs 50) at the rate 150 from market. If it gives20% dividend what is effective return?
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728 views

Bit tricky plot on GRE

In a city 90% of the population own a car, 15% own a motor cycle, and everybody owns one or the other or both. Find the percentage of motorcycle owners to car owners. In order to solve it i have ...
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3answers
522 views

Tricky Question from GRE using Ratios

Of two kinds of alloy, silver and copper are contained in the ratio of $5:1$ and the other in $7:2$. What weights of the two alloys should be melted and mixed together so as to makeup a $5$ lb mass ...
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1answer
81 views

Meaningful statistic measure of data pairs

I have a dilemma. I have pairwise data, (a,b), that represents some form of speed, whether it's miles/hour or megabits/second. Let's say that we have the following set of data from measuring the "...
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1answer
33 views

Simple Question: division of sums

I am a little bit confused about the following simple task. Given some functions $f(x), g(x), h(x), l(x), m(x)$. We know that $\frac{f(x)}{g(x)}= m(x)$. We further know that $h(x), l(x)$ are ...
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2answers
902 views

Proportion questions related fourth proportions

I have a couple of basic Proportion questions that I am unable to solve. 18 men build a wall that is 140m long in 42 days. How long would it take 30 men to build a wall that is 100m long? In a ...
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1answer
20 views

Problem with the answer of a basic ratio problem

Here is the solved example. The answer given is 175, but my calculation comes out to be 375. I thought that it was just a typo, but it has been written twice, so I'm not sure. What am I doing wrong?
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563 views

How do I calculate the aspect ratio of a width and height?

I am creating an image upload form. I want to restrict users from uploading images that are not of the aspect ratio of 16:9. What is the formula for calculating an aspect ratio such as this? If w = ...
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1answer
111 views

Turning an angle into a ratio of squares left/right:squares up/down

I'm a 9th grader in Algebra 1 right now and in my spare time I like programming, I am trying to re-create the game Pong right now but I am having a little problem. I know I am asking a question about ...
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1answer
52 views

what do these odds ratios represent?

I am reading this article in which is given the matrix of the joint probabilities of two random variables, X=$(x_1,x_2)$ and Y=$(y_1,y_2)$. Let's say they are $(p_{1,1},p_{1,2},p_{2,1},p_{2,2})$. ...
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75 views

Simple real life problem

Let say my girlfriend makes $2000$ Euros per month and I make $3400$ Euros, let say all our living costs sum up to $1540$ Euros. How can i calculate how much each of us must pay (off the $1540$ Euros) ...
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1k views

Proving Ratios And Proportions

Help me solve this problem! I have tried it many times but nothing appeared. This is the question: If a:b=c:d=e:f, prove that each is equal to (a+c-e):(b+d-f).
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1answer
184 views

Ratio of area between similar triangles

This question has nearly no information and I've been stuck on this for quite some time. I tried drawing the median from A thru G but the 1x to 2x ratio didn't seem to help.
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1answer
227 views

ratio distribution of gamma with different parameter

Let $X$ be gamma distributed random variable with parameters $a$ and $b$. Let $W$ be gamma distributed random variable with parameters $c$ and $d$, such that \begin{equation} f_X(x) = \frac{x^{a-1}e^{-...
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2answers
280 views

Real Analysis: Limit Proof with help of ratio convergence property

The thing is to, using the property above, prove the expression below. First tried to obtain the difference between n and n+1 terms, then factored out n+1 ^ p and rearanged the sequence. I've ...
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Equation with logarithms and absolute value

I have this equation: $$ \ln\frac{2-|y-1|}{1-|y|} = \ln x $$ which becomes $$ \ln(2-|y-1|)-\ln(1-|y|) = \ln x. $$ Can the first term in LHS be written as $\ln(2)-\ln(|y-1|)\implies\ln(2)-\ln(|y|)-\...
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1answer
51 views

Finding the alternate forms of ratios

This is a super basic algebra question but I can't figure out how you get the alternate form of: $$\frac ab = \frac cd$$ Which is: $$\frac {a+b}b = \frac{c+d}d$$ The process explaining how we ...
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1answer
778 views

How to Calculate gear ratio for potentiometer

I am not a mathematician so please bare this in mind. I am designing a computer steering wheel, using real car parts (fitting the steering wheel from a hatchback via gears to a potentiometer which is ...
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1answer
65 views

Shared groceries expenses between roommates to be divided as per specific consumption ratio and attendance

My apologies if this question is in the wrong section. Couple of my roommates & I (total 5 people) share the groceries expenses. We record the purchases in an Excel sheet, and also have the ratio ...
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3answers
124 views

How many boys, girls, men and women are there?

In a village, there are exactly $10$% more boys than girls; $15$% more women than men; $20$% more children than adults. The population is less than $6000$. Solution: $b = g + 0.1g$--------(i), where ...
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1answer
71 views

Expressing a decimal percentage as a ratio

Maths newbie here. How would I express a decimal percentage such as 90.3 as a ratio ("one in...")? I've done a search and the explanations aren't too clear at all. I'm about to enrol on to a ...
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1answer
80 views

Selling Corrupt quality of honey with allegation…

I have a problem that uses Allegation concept, I tried it I would like to know If I am Correct..? A Honey seller gets pure honey($1$ Litre ) for $100$ and a sweet oil for $20$ he shall mix honey ...
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2k views

Ratios as Fractions

I’m having trouble understanding how fractions relate to ratios. A ratio like 3:5 isn’t directly related to the fraction 3/5, is it? I see how that ratio could be expressed in terms of the two ...
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4answers
101 views

Why does $\tfrac{a}{b} = \tfrac{c}{d} = \tfrac{e}{f} \rightarrow \tfrac{a}{b} = \tfrac{c-e}{d-f}$

Why is it that $$\frac{a}{b} = \frac{c}{d} = \frac{e}{f} \rightarrow \frac{a}{b} = \frac{c-e}{d-f}$$ It is used in the proof of Ceva's theorem. Thank you.
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Contradictory definitions of ratio

How is the word ratio defined? I know of two different interpretations of the term ratio, and they are somewhat contradictory. They are: 1) The Reynolds number is the ratio of inertial force to ...
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7k views

Dividing line segments with ratios vs. fractions [closed]

I know that $2:3$ is actually $\frac {2}{3}$. So when you split a line segment by a ratio, you would add $2$ and $3$ to get a fraction of $\frac {2}{5}$ that will be used to solve the problem. I can'...
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2answers
129 views

Splitting a segment with a ratio

I came across the homework question that I attempted to do. After looking at the answers, and getting it wrong I didn't understand why. I'm specifically lost at why we would get a fraction of 2/5 at ...
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1answer
68 views

Given a value and an arbitrary range, finding equivalent value in other arbitrary range

While strictly related to a programming project of mine, the problem in itself boils down to a math problem, as I am not sure which steps to take to produce the results i need. I have an input value (...
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76 views

Should ratio definition have these words, of the same kind?

This is the definition of ratio that is on Wikipedia. “a ratio is a relationship between two numbers of the same kind” Considering the ratio of a moving distance to the fuel amount in a vehicle, ...
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1answer
4k views

Consistency of a ratio between positive and negative numbers

I want to model the inverse relationship between two sets of numbers $A, B$ both in the domain $[-5, 5]$. That is, for the same value $A$ I need a number that decreases linearly as $B$ increases, ...