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

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

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

Find Two Numbers

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

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: #one double the other

a:b=2:3

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

no such category found: #a/b;⅔

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

no such category found: #a/b;⅔

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

no such category found: #a/b;⅔

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

no such category found: #a/b;⅔

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

no such category found: #a/b;⅔

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

no such category found: #a/b;⅔
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$\scriptstyle\begin{cases}\scriptstyle a:b=2:3\\\scriptstyle\left(a\sdot b\right)^2=b\sdot\sqrt{8}\end{cases}$

no such category found: #a/b;⅔

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

no such category found: #a/b;⅔

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

no such category found: #a/b;⅔

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

no such category found: #a/b;⅔

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

no such category found: #a/b;⅔

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

no such category found: #a/b;⅔

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

no such category found: #a/b;⅔

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

no such category found: #a/b;⅔

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

no such category found: #a/b;⅔

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

no such category found: #a/b;⅔

a:b=3:4

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

no such category found: #a/b;¾

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

no such category found: #a/b;¾

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

no such category found: #a/b;¾

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

no such category found: #a/b;¾

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

no such category found: #a/b;¾

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

no such category found: #a/b;¾

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

no such category found: #a/b;¾

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: #a/b;⅘

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

no such category found: #a/b;⅘

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: #a/b;⅗

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

no such category found: #a/b;⅗

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

no such category found: #a/b;⅗

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

no such category found: #a/b;⅗

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

no such category found: #a/b;⅗

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: #a/b;⅖

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: #a/b;¼

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: #a/b;⅓

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

three proportional numbers, a·b·c=1000

no such category found: #three proportional numbers