Difference between revisions of "Find a Number Problems"

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== Find Three Numbers ==
 
== Find Three Numbers ==
  
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<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle a+b=c\\\scriptstyle a+c=100b\end{cases}</math><div class="mw-collapsible-content">
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[[comment: a+b=c;a+c=100b]]
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<div class="mw-collapsible mw-collapsed"><math>\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}</math><div class="mw-collapsible-content">
 
<div class="mw-collapsible mw-collapsed"><math>\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}</math><div class="mw-collapsible-content">
 
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Revision as of 08:16, 2 March 2022

Category Comment Link Annotated text
word problem/find a numberrepeated subtractionמלאכת_המספר#TEa8Question: 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 numberrepeated subtractionספר_חשבון#QPoGIf one asks you: 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 numberrepeated subtractionמלאכת_המספר#j27HQuestion: 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 number⅓a+⅕a=10מלאכת_המספר#niUjSuppose 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)=20
Category Comment Link Annotated text
word problem/find a number⅓a+¼a=20מלאכת_המספר#AuztExample: 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 number⅓a+¼a=6מלאכת_המספר#m65tExample: 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 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=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: #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
}}


\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=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

three proportional numbers, a·b·c=1000
no such category found: #three proportional numbers
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