Find a Number Problems

Category	Comment	Link	Annotated text
word problem/find a number	repeated subtraction	מלאכת_המספר#TEa8	Question: if we subtract 12 from the double of any number, then we subtract another 12 from double the remainder also, and double the remainder is 12, how much is the original number? :$\scriptstyle2\sdot\left[\left[2\sdot\left(2X-12\right)\right]-12\right]=12$ שאילה אם מכפלו של אי זה מספר נקח י"ב ומכפל הנשאר נקח ג"כ י"ב אחרי' וכפל הנשאר יהיה י"ב כמה היה המספר הראשון
word problem/find a number	repeated subtraction	ספר_חשבון#QPoG	A number, you subtract a tenth from it, then you subtract again a tenth from the remainder, and 100 are left. :How much was the original number before subtracting the two tenths? :$\scriptstyle X-\frac{1}{10}X-\left[\frac{1}{10}\sdot\left(X-\frac{1}{10}X\right)\right]=100$ אם ישאלך אדם חשבון שהסרות ממנו הי' ומן הנשאר הסרות ממנו העשירית פעם שנית ונשארו ק‫' כמה היה כל החשבון בטרם שהסרת ממנו ב' העשיריות
word problem/find a number	repeated subtraction	מלאכת_המספר#j27H	Question: if the half of any amount plus one are subtracted, then the half of the remainder plus one, then the half of the remainder plus one, and one remains, how much is the original number? שאילה אם מאי זה כמות ילקח חציו ואחד יותר ומהנשאר חציו ויותר אחד ומהנשאר חציו ויותר אחד ונשאר אחד כמה היה המספר הראשון |} :$\scriptstyle\left[\left[X-\left(\frac{1}{2}X+1\right)\right]-\left[\left[\frac{1}{2}\sdot\left[X-\left(\frac{1}{2}X+1\right)\right]\right]+1\right]\right]-\left[\left[\frac{1}{2}\sdot\left[\left[X-\left(\frac{1}{2}X+1\right)\right]-\left[\left[\frac{1}{2}\sdot\left[X-\left(\frac{1}{2}X+1\right)\right]\right]+1\right]\right]\right]+1\right]=1$

Find One Number

$\scriptstyle\left(\frac{1}{3}\sdot a\right)+\left(\frac{1}{5}\sdot a\right)=10$

Category	Comment	Link	Annotated text
word problem/find a number	⅓a+⅕a=10	מלאכת_המספר#niUj	Suppose we want to find any whole, such that the sum of its third and its fifth together is ten. :$\scriptstyle\frac{1}{3}X+\frac{1}{5}X=10$ נניח שרצינו למצא אי זה כל שקבוץ שלישיתו וחמישיתו יחד הם עשרה

$\scriptstyle\left(\frac{1}{3}\sdot a\right)+\left(\frac{1}{4}\sdot a\right)=10+\frac{1}{2}$

Category	Comment	Link	Annotated text
word problem/find a number	⅓a+¼a=10½	מלאכת_המספר#IQCS	Example for this: suppose the sum of a third and a quarter of the whole is equal to ten and a half and we wish to know the whole. :$\scriptstyle\frac{1}{3}X+\frac{1}{4}X=10+\frac{1}{2}$ המשל לזה נניח קבוץ אחד משליש ורביע ששוה עשרה וחצי ורצינו לדעת הכל

$\scriptstyle\left(\frac{1}{3}\sdot a\right)+\left(\frac{1}{4}\sdot a\right)=20$

Category	Comment	Link	Annotated text
word problem/find a number	⅓a+¼a=20	מלאכת_המספר#Auzt	Example: we wish to find a number that the sum of its third and its quarter is 20. :$\scriptstyle\frac{1}{3}X+\frac{1}{4}X=20$ המשל רצינו למצא מספר שקבוץ שלישיתו ורביעיתו יהיה כ‫'

$\scriptstyle\left(\frac{1}{3}\sdot a\right)+\left(\frac{1}{4}\sdot a\right)=6$

Category	Comment	Link	Annotated text
word problem/find a number	⅓a+¼a=6	מלאכת_המספר#m65t	Example: we wish to find a number, whose quarter and third are 6. :$\scriptstyle\frac{1}{3}X+\frac{1}{4}X=6$ המשל רצינו למצא מספר אחד שרביעיתו ושלישיתו יהיה ו‫'

$\scriptstyle\left(\frac{1}{4}\sdot a\right)+\left(\frac{1}{5}\sdot a\right)=5$

Category	Comment	Link	Annotated text
word problem/find a number	¼a+⅕a=5	מלאכת_המספר#0Nd6	As the one who asks about the sum of a quarter and a fifth [of a whole], which is 5 integers, and we wish to know how much is the whole. :$\scriptstyle\frac{1}{4}X+\frac{1}{5}X=5$ כמי שישאל על קבוץ רביע וחומש שהם ה' שלימי' ונרצה לדעת הכל כמה הוא

$\scriptstyle a-\left(\frac{1}{3}\sdot a\right)=\sqrt{a}$

no such category found: #find one number

$\scriptstyle\left[a-\left(\frac{2}{3}\sdot a\right)\right]^2=20$

no such category found: #find one number

$\scriptstyle\left[a\sdot\left(\frac{2}{3}\sdot a\right)\right]^2=36$

no such category found: #find one number

$\scriptstyle a^2\sdot\left(\frac{3}{4}\sdot a^2\right)=6a$

no such category found: #find one number

$\scriptstyle a+28=2a^2$

no such category found: #find one number

$\scriptstyle a^2\sdot a=12a+10a^2$

no such category found: #find one number

$\scriptstyle\sqrt{9a}=12$

no such category found: #find one number

$\scriptstyle\left(a\sdot\frac{2}{3}a\right)^2=\sqrt{50}$

no such category found: #find one number

$\scriptstyle\left(a\sdot\frac{2}{3}a\right)\sdot a=a\sdot\sqrt{8}$

no such category found: #find one number

$\scriptstyle\frac{3}{7}a+\frac{4}{5}a=\frac{2}{3}a+\frac{1}{4}a+20$

Category	Comment	Link	Annotated text
word problem/find a number	³/₇a+⁴/₅a=⅔a+¼a+20	ספר_מעשה_חושב#7YKC	Example: three-sevenths and four-fifths of the unknown number exceed two-thirds and a quarter of the unknown number by twenty and we wish to know how much is the number? ::$\scriptstyle\frac{3}{7}a+\frac{4}{5}a=\frac{2}{3}a+\frac{1}{4}a+20$ דמיון זה שיהיו ג' שביעיות וד' חמישיות המספר הנעלם מוסיפים על ב' שלישיות ורביעית המספר הנעלם עשרים ורצינו לדעת כמה המספר
word problem/find a number	³/₇a+⁴/₅a=⅔a+¼a+20	ספר_דיני_ממונות#SkQW	46) Question: three sevenths and four fifths of the unknown number exceed two thirds and a quarter of the unknown number by twenty. :We wish to know: how much is the number? :$\scriptstyle\frac{3}{7}a+\frac{4}{5}a=\frac{2}{3}a+\frac{1}{4}a+20$ מו) שאלה ג' שביעיות וד' חמישיות המספר הנעלם מוסיפים על ב' שלישיות ורביעית המספר הנעלם כ‫' רצינו לדעת כמה המספר הנעלם

$\scriptstyle\frac{3a}{4}:4=4:6$

no such category found: #find one number

$\scriptstyle4=\frac{1}{3}\sdot15\longrightarrow a=\frac{1}{5}\sdot25$

no such category found: #find one number

Find Two Numbers

$\scriptstyle\begin{cases}\scriptstyle b-1=a+1\\\scriptstyle2\sdot\left(a-1\right)=b+1\end{cases}$

no such category found: #find two numbers

$\scriptstyle\begin{cases}\scriptstyle b-1=a+1\\\scriptstyle20\sdot\left(a-1\right)=b+1\end{cases}$

no such category found: #find two numbers

$\scriptstyle\begin{cases}\scriptstyle2\sdot\left(b-1\right)=a+1\\\scriptstyle3\sdot\left(a-1\right)=b+1\end{cases}$

no such category found: #find two numbers

$\scriptstyle\begin{cases}\scriptstyle a^2=b-5\\\scriptstyle a^2+b^2=100\end{cases}$

no such category found: #find two numbers

$\scriptstyle\begin{cases}\scriptstyle a^2=2b+8\\\scriptstyle a^2+b^2=80\end{cases}$

no such category found: #find two numbers

b=2a

$\scriptstyle\begin{cases}\scriptstyle b=2a\\\scriptstyle a^2\sdot b=9b\end{cases}$

no such category found: #find two numbers

a:b=2:3

$\scriptstyle\begin{cases}\scriptstyle a:b=2:3\\\scriptstyle4a+4b=\sqrt{100}\end{cases}$

no such category found: #find two numbers

$\scriptstyle\begin{cases}\scriptstyle a:b=2:3\\\scriptstyle a\sdot b=\sqrt{12}\end{cases}$

no such category found: #find two numbers

$\scriptstyle\begin{cases}\scriptstyle a:b=2:3\\\scriptstyle\left(3a+4b\right)\sdot\sqrt{5}=40\end{cases}$

no such category found: #find two numbers

$\scriptstyle\begin{cases}\scriptstyle a:b=2:3\\\scriptstyle\left(a\sdot b\right)\sdot\sqrt{8}=100\end{cases}$

no such category found: #find two numbers

$\scriptstyle\begin{cases}\scriptstyle a:b=2:3\\\scriptstyle a\sdot\sqrt{a}=2b\end{cases}$

no such category found: #find two numbers

$\scriptstyle\begin{cases}\scriptstyle a:b=2:3\\\scriptstyle a\sdot\sqrt{a}=b^2\end{cases}$

no such category found: #find two numbers

$\scriptstyle\begin{cases}\scriptstyle a:b=2:3\\\scriptstyle\left(a\sdot b\right)^2=b\sdot\sqrt{8}\end{cases}$

no such category found: #find two numbers

$\scriptstyle\begin{cases}\scriptstyle a:b=2:3\\\scriptstyle a^2\sdot b=b\sdot\sqrt{b}\end{cases}$

no such category found: #find two numbers

$\scriptstyle\begin{cases}\scriptstyle a:b=2:3\\\scriptstyle5a+7b=16+\sqrt{8}\end{cases}$

no such category found: #find two numbers

$\scriptstyle\begin{cases}\scriptstyle a:b=2:3\\\scriptstyle3a+4\sqrt{b}=30\end{cases}$

no such category found: #find two numbers

$\scriptstyle\begin{cases}\scriptstyle a:b=2:3\\\scriptstyle a\sdot b=20+\sqrt{8}\end{cases}$

no such category found: #find two numbers

$\scriptstyle\begin{cases}\scriptstyle a:b=2:3\\\scriptstyle\left(a\sdot b\right)\sdot b=100+\sqrt{8}\end{cases}$

no such category found: #find two numbers

$\scriptstyle\begin{cases}\scriptstyle a:b=2:3\\\scriptstyle\left(a^2\sdot b\right)+\sqrt{a^2\sdot b}=342\end{cases}$

no such category found: #find two numbers

$\scriptstyle\begin{cases}\scriptstyle a:b=2:3\\\scriptstyle\left(a\sdot b\right)^2=20+\sqrt{30}\end{cases}$

no such category found: #find two numbers

$\scriptstyle\begin{cases}\scriptstyle a:b=2:3\\\scriptstyle\left(a\sdot b\right)^2+\left(a^2\sdot\sqrt{4}\right)=4+\frac{1}{4}\end{cases}$

no such category found: #find two numbers

$\scriptstyle\begin{cases}\scriptstyle a:b=2:3\\\scriptstyle3a+4b=\sqrt[3]{216}\end{cases}$

no such category found: #find two numbers

a:b=3:4

$\scriptstyle\begin{cases}\scriptstyle a:b=3:4\\\scriptstyle a^2\sdot b=288\end{cases}$

no such category found: #find two numbers

$\scriptstyle\begin{cases}\scriptstyle a:b=3:4\\\scriptstyle\left(a\sdot b\right)\sdot\left(a+b\right)=a^2\end{cases}$

no such category found: #find two numbers

$\scriptstyle\begin{cases}\scriptstyle a:b=3:4\\\scriptstyle a^2\sdot b=\sqrt{20+\frac{1}{4}}\end{cases}$

no such category found: #find two numbers

$\scriptstyle\begin{cases}\scriptstyle a:b=3:4\\\scriptstyle8a=6\sqrt{b}\end{cases}$

no such category found: #find two numbers

$\scriptstyle\begin{cases}\scriptstyle a:b=3:4\\\scriptstyle\left(a\sdot\sqrt{8}\right)+b^2=48\end{cases}$

no such category found: #find two numbers

$\scriptstyle\begin{cases}\scriptstyle a:b=3:4\\\scriptstyle\left(a\sdot b\right)^2+27=9b^2\end{cases}$

no such category found: #find two numbers

$\scriptstyle\begin{cases}\scriptstyle a:b=3:4\\\scriptstyle\sqrt[3]{2a+3b}=8\end{cases}$

no such category found: #find two numbers

a:b=4:5

$\scriptstyle\begin{cases}\scriptstyle a:b=4:5\\\scriptstyle\left(a\sdot b\right)^2=a^2\sdot b\end{cases}$

no such category found: #find two numbers

$\scriptstyle\begin{cases}\scriptstyle a:b=4:5\\\scriptstyle a\sdot b=b\sdot\sqrt{8}\end{cases}$

no such category found: #find two numbers

a:b=3:5

$\scriptstyle\begin{cases}\scriptstyle a:b=3:5\\\scriptstyle\left(a\sdot b\right)^2=a^2\end{cases}$

no such category found: #find two numbers

$\scriptstyle\begin{cases}\scriptstyle a:b=3:5\\\scriptstyle\left[\left(a\sdot\sqrt{a}\right)+\left(b\sdot\sqrt{b}\right)\right]\sdot\sqrt{8}=100\end{cases}$

no such category found: #find two numbers

$\scriptstyle\begin{cases}\scriptstyle a:b=3:5\\\scriptstyle\left(a\sdot b\right)\sdot\sqrt{8}=b\end{cases}$

no such category found: #find two numbers

$\scriptstyle\begin{cases}\scriptstyle a:b=3:5\\\scriptstyle a^2\sdot b=b^2\sdot\sqrt{8}\end{cases}$

no such category found: #find two numbers

$\scriptstyle\begin{cases}\scriptstyle a:b=3:5\\\scriptstyle a\sdot b=\sqrt[3]{729}\end{cases}$

no such category found: #find two numbers

a:b=2:5

$\scriptstyle\begin{cases}\scriptstyle a:b=2:5\\\scriptstyle a\sdot b=8\sqrt{b}\end{cases}$

no such category found: #find two numbers

a:b=1:4

$\scriptstyle\begin{cases}\scriptstyle a:b=1:4\\\scriptstyle\left(a\sdot b\right)\sdot a=\sqrt[3]{216}\end{cases}$

no such category found: #find two numbers

a:b=1:3

$\scriptstyle\begin{cases}\scriptstyle a:b=1:3\\\scriptstyle\sqrt[3]{a}\sdot\sqrt[3]{b}=100\end{cases}$

no such category found: #find two numbers

a:b=5:7

$\scriptstyle\begin{cases}\scriptstyle a:b=5:7\\\scriptstyle\left(a\sdot b\right)^2=a^2\sdot\sqrt{8}\end{cases}$

no such category found: #find two numbers

Find Three Numbers

$\scriptstyle\begin{cases}\scriptstyle a+b=c\\\scriptstyle a+c=100b\end{cases}$

no such category found: #find three numbers

$\scriptstyle\begin{cases}\scriptstyle a:b=2:3\\\scriptstyle b:c=3:4\\\scriptstyle\left(a^2\sdot a\right)+b^2=\left(12+\frac{1}{2}\right)\sdot c\end{cases}$

no such category found: #a/b/c;2/3/4

$\scriptstyle\begin{cases}\scriptstyle\left(a+b\right):c=3+\frac{2}{5}+\frac{1}{7}\\\scriptstyle\left(a+c\right):b=7+\frac{2}{3}+\frac{1}{4}\\\scriptstyle b=30\end{cases}$

no such category found: #find three numbers

$\scriptstyle\begin{cases}\scriptstyle\left(a+b\right):c=\frac{3}{5}+\frac{1}{6}\\\scriptstyle\left(a+c\right):b=2+\frac{1}{3}\\\scriptstyle a=20\end{cases}$

no such category found: #find three numbers

$\scriptstyle\begin{cases}\scriptstyle b:\left(c-a\right)=3+\frac{1}{3}\\\scriptstyle c:\left(b-a\right)=6\end{cases}$

no such category found: #find three numbers

$\scriptstyle\begin{cases}\scriptstyle\left(a+b\right):\left(c-a\right)=4+\frac{1}{2}\\\scriptstyle\left(a+c\right):\left(b-a\right)=5\end{cases}$

no such category found: #find three numbers

$\scriptstyle\begin{cases}\scriptstyle a+\frac{1}{4}\sdot\left(b+c\right)=b+\frac{1}{6}\sdot\left(a+c\right)=c+\frac{1}{9}\sdot\left(a+b\right)\\\scriptstyle b=20\end{cases}$

no such category found: #find three numbers

three proportional numbers, a·b·c=1000

no such category found: #three proportional numbers