Difference between revisions of "Find a Number Problems"

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(→‎Find Three Numbers)
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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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[[comment: (a+b)\c=3⅖⅐;(a+c)\b=7⅔¼;b=30]]
 
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<div class="mw-collapsible mw-collapsed"><math>\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}</math><div class="mw-collapsible-content">
 
<div class="mw-collapsible mw-collapsed"><math>\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}</math><div class="mw-collapsible-content">
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[[comment: (a+b)/c=⅗+⅙;(a+c)/b=2⅓;a=20]]
 
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<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle b:\left(c-a\right)=3+\frac{1}{3}\\\scriptstyle c:\left(b-a\right)=6\end{cases}</math><div class="mw-collapsible-content">
 
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle b:\left(c-a\right)=3+\frac{1}{3}\\\scriptstyle c:\left(b-a\right)=6\end{cases}</math><div class="mw-collapsible-content">
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<div class="mw-collapsible mw-collapsed"><math>\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}</math><div class="mw-collapsible-content">
 
<div class="mw-collapsible mw-collapsed"><math>\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}</math><div class="mw-collapsible-content">
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[[comment: (a+b)/(c-a)=4½;(a+c)/(b-a)=5]]
 
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<div class="mw-collapsible mw-collapsed"><math>\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}</math><div class="mw-collapsible-content">
 
<div class="mw-collapsible mw-collapsed"><math>\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}</math><div class="mw-collapsible-content">
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[[comment: a+¼(b+c)=b+⅙(a+c)=c+⅑(a+b);b=20]]
 
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<div class="mw-collapsible mw-collapsed">three proportional numbers, a·b·c=1000<div class="mw-collapsible-content">
 
<div class="mw-collapsible mw-collapsed">three proportional numbers, a·b·c=1000<div class="mw-collapsible-content">
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Revision as of 10:04, 26 September 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#QPoGA 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)=10+\frac{1}{2}
Category Comment Link Annotated text
word problem/find a number⅓a+¼a=10½מלאכת_המספר#IQCSExample 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 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\left(\frac{1}{4}\sdot a\right)+\left(\frac{1}{5}\sdot a\right)=5
Category Comment Link Annotated text
word problem/find a number¼a+⅕a=5מלאכת_המספר#0Nd6As 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 number³/₇a+⁴/₅a=⅔a+¼a+20ספר_מעשה_חושב#7YKCExample: 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 number³/₇a+⁴/₅a=⅔a+¼a+20ספר_דיני_ממונות#SkQW46) 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

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

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