Difference between revisions of "Find a Number Problems"

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Revision as of 08:23, 6 October 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 a Perfect Number

perfect number
Category Comment Link Annotated text
word problem/find a numberperfect numberספר_דיני_ממונות#x3Is109) If you want to find the second [perfect number] קט)‫MS L: om. ואם תרצה למצא השני
word problem/find a numberperfect numberספר_דיני_ממונות#IXt8108) Question: if you want to find a perfect number קח) שאלה אם תרצה למצא {{#annot:term|75|xt6c}}מספר שלם{{#annotend:xt6c}} נקרא בלשונם {{#annot:term|75|aiWm}}נומירו פירפיטו{{#annotend:aiWm}}
word problem/find a numberperfect numberספר_דיני_ממונות#CaJp110) If you want to find the third [perfect number] קי)‫MS L: om. ואם ואם תרצה למצא השלישי

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


\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


\scriptstyle a^2=40+\frac{41}{b}
no such category found: #find one number


\scriptstyle a\bmod3=a\bmod5=a\bmod7=1
Category Comment Link Annotated text
word problem/find a numbera(mod)3=a(mod5)=a(mod7)=1ספר_דיני_ממונות#lQns168) Question: find me a number, such that if you divide it by 3, by 5, and by 7, 1 remains. קסח) שאלה בקש לי מספר שאם תחלקהו על ג' ועל ה ועל ז' ישאר א‫'


\scriptstyle a\bmod3=2;a\bmod5=4;a\bmod7=6
Category Comment Link Annotated text
word problem/find a numbera(mod)3=2,a(mod5)=4,a(mod7)=6ספר_דיני_ממונות#hx8d169) Question: if you are told that the remainder after casting out the threes is 2 etc. :Do it this way: :For instance, if it is said that when we divide it by 3, 2 remains; if its is divided by 5, 4 remains; and if it is divided by 7, 6 remains. קסט) שאלה ואם אמר לך שנשאר בהשליכך ג"ג ב' או ג‫'
עשה בדרך הזה
עד"מ ואם אמר כשנחלקהו על ג' ישאר ב' ואם יחולק על ה' ישאר ד' ואם יחולק על ז' ישאר ו‫'


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: #find three numbers

\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

\scriptstyle\begin{cases}\scriptstyle a:b=b:c\\\scriptstyle a\sdot b\sdot c=1000\end{cases}
no such category found: #find three numbers

Find Six Numbers

six proportional numbers
Category Comment Link Annotated text
word problem/find a numbersix proportional numbersספר_דיני_ממונות#WrirFor example: we have six proportional numbers, the first is 2 and the sixth is 64. ::We wish to know which is the second. דמיון זה יש לנו ו' {{#annot:term|994,1277|VUeX}}מספרים מתיחסים{{#annotend:VUeX}} הראשון ב' והו' ס"ד
נרצה לדעת מהו השני
word problem/find a numbersix proportional numbersספר_דיני_ממונות#FvyIExample: the first is 2-[eighths] and the sixth is 256 integers. דמיון הראשון ב' שלישיות והו' רנ"ו שלמים
word problem/find a numbersix proportional numbersספר_דיני_ממונות#fNcEExample: we have six proportional numbers, the first of which is 2 and the sixth is 64. דמיון יש לנו ו' מספרים מתיחסים שהראשון ב' והו' ס"ד
word problem/find a numbersix proportional numbersספר_דיני_ממונות#Yfpk111) Question: if you want to find a proportional number: :For example: we have six proportional numbers, i.e. the ratio of the sixth to the fifth is the same as the ratio of the fifth to the fourth, and the same as the ratio of the fourth to the third, and the same as the ratio of the third to the second, and the same as the ratio of the second to the first. :The first number is 2. :The sixth is 2048. :We wish to know how much is the second? קיא)‫MS L: קט שאלה אם תרצה למצא {{#annot:term|994,2263|2xtB}}מספר יחסיי{{#annotend:2xtB}} הנקרא בלשונם {{#annot:term|994|DhLM}}נומירו פרופורציאונלי{{#annotend:DhLM}}
דמיון זה יש לנו ו' {{#annot:term|994,2263|jjwV}}מספרים יחסיים{{#annotend:jjwV}} ר"ל שיחס הו' אל הה' כיחס הה' אל הד' וכיחס הד' אל הג' וכיחס הג' אל הב' וכיחס הב' אל הא‫'
והמספר הא' ב‫'
והו' ב' אלפים ומ"ח
ונרצה לדעת מהו השני

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