Difference between revisions of "Find a Number Problems"

Revision as of 17:05, 9 October 2022

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	If 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 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 a Perfect Number

[Expand]perfect number

Find One Number

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

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

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

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

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

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

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

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

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

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\scriptstyle a+28=2a^2

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

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\scriptstyle\sqrt{9a}=12

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

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

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

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

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

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\scriptstyle a^2=40+\frac{41}{b}

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\scriptstyle a\bmod3=a\bmod5=a\bmod7=1

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\scriptstyle a\bmod3=2;a\bmod5=4;a\bmod7=6

Find Two Numbers

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

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

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

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

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

b=2a

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

a:b=2:3

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

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

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

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

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

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

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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}

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

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

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

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

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

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

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

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\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}

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

a:b=3:4

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

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

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

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

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

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

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

a:b=4:5

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

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

a:b=3:5

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

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\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}

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

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

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

a:b=2:5

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

a:b=1:4

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

a:b=1:3

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

a:b=5:7

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

Find Three Numbers

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

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\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}

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\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}

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\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}

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

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\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}

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\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}

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\scriptstyle\begin{cases}\scriptstyle a:b=b:c\\\scriptstyle a\sdot b\sdot c=1000\end{cases}

Find Six Numbers

[Expand]six proportional numbers

Category	Comment	Link	Annotated text
word problem/find a number	six proportional numbers	ספר_דיני_ממונות#Wrir	For 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 number	six proportional numbers	ספר_דיני_ממונות#FvyI	Example: the first is 2-[eighths] and the sixth is 256 integers. דמיון הראשון ב' שלישיות והו' רנ"ו שלמים
word problem/find a number	six proportional numbers	ספר_דיני_ממונות#fNcE	Example: 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 number	six proportional numbers	ספר_דיני_ממונות#Yfpk	111) 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

@@ Line 47: / Line 47: @@
 <div class="mw-collapsible mw-collapsed"><math>\scriptstyle a-\left(\frac{1}{3}\sdot a\right)=\sqrt{a}</math><div class="mw-collapsible-content">
 {{#annotask:
-	[[category: #find one number]]
+	[[category: #find a number]]
 	[[comment: a-⅓a=√a]]
 }}</div></div>
@@ Line 53: / Line 53: @@
 <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left[a-\left(\frac{2}{3}\sdot a\right)\right]^2=20</math><div class="mw-collapsible-content">
 {{#annotask:
-	[[category: #find one number]]
+	[[category: #find a number]]
 	[[comment: (a-⅓a)²=20]]
 }}</div></div>
@@ Line 59: / Line 59: @@
 <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left[a\sdot\left(\frac{2}{3}\sdot a\right)\right]^2=36</math><div class="mw-collapsible-content">
 {{#annotask:
-	[[category: #find one number]]
+	[[category: #find a number]]
 	[[comment: (a·⅔a)²=36]]
 }}</div></div>
@@ Line 65: / Line 65: @@
 <div class="mw-collapsible mw-collapsed"><math>\scriptstyle a^2\sdot\left(\frac{3}{4}\sdot a^2\right)=6a</math><div class="mw-collapsible-content">
 {{#annotask:
-	[[category: #find one number]]
+	[[category: #find a number]]
 	[[comment: a²·¾a²=6a]]
 }}</div></div>
@@ Line 71: / Line 71: @@
 <div class="mw-collapsible mw-collapsed"><math>\scriptstyle a+28=2a^2</math><div class="mw-collapsible-content">
 {{#annotask:
-	[[category: #find one number]]
+	[[category: #find a number]]
 	[[comment: a+28=2a²]]
 }}</div></div>
@@ Line 77: / Line 77: @@
 <div class="mw-collapsible mw-collapsed"><math>\scriptstyle a^2\sdot a=12a+10a^2</math><div class="mw-collapsible-content">
 {{#annotask:
-	[[category: #find one number]]
+	[[category: #find a number]]
 	[[comment: a²·a=12a+10a²]]
 }}</div></div>
@@ Line 83: / Line 83: @@
 <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{9a}=12</math><div class="mw-collapsible-content">
 {{#annotask:
-	[[category: #find one number]]
+	[[category: #find a number]]
 	[[comment: √(9a)=12]]
 }}</div></div>
@@ Line 89: / Line 89: @@
 <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(a\sdot\frac{2}{3}a\right)^2=\sqrt{50}</math><div class="mw-collapsible-content">
 {{#annotask:
-	[[category: #find one number]]
+	[[category: #find a number]]
 	[[comment: (a·⅔a)²=√50]]
 }}</div></div>
@@ Line 95: / Line 95: @@
 <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(a\sdot\frac{2}{3}a\right)\sdot a=a\sdot\sqrt{8}</math><div class="mw-collapsible-content">
 {{#annotask:
-	[[category: #find one number]]
+	[[category: #find a number]]
 	[[comment: (a·⅔a)·a=a√8]]
 }}</div></div>
@@ Line 107: / Line 107: @@
 <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{3a}{4}:4=4:6</math><div class="mw-collapsible-content">
 {{#annotask:
-	[[category: #find one number]]
+	[[category: #find a number]]
 	[[comment: (3a/4)/4=4/6]]
 }}</div></div>
@@ Line 113: / Line 113: @@
 <div class="mw-collapsible mw-collapsed"><math>\scriptstyle4=\frac{1}{3}\sdot15\longrightarrow a=\frac{1}{5}\sdot25</math><div class="mw-collapsible-content">
 {{#annotask:
-	[[category: #find one number]]
+	[[category: #find a number]]
 	[[comment: 4=⅓·15→a=⅕·25]]
 }}</div></div>
@@ Line 119: / Line 119: @@
 <div class="mw-collapsible mw-collapsed"><math>\scriptstyle a^2=40+\frac{41}{b}</math><div class="mw-collapsible-content">
 {{#annotask:
-	[[category: #find one number]]
+	[[category: #find a number]]
 	[[comment: a²=40+41\b]]
 }}</div></div>

Difference between revisions of "Find a Number Problems"

Revision as of 17:05, 9 October 2022

Contents

Find a Perfect Number

Find One Number

Find Two Numbers

b=2a

a:b=2:3

a:b=3:4

a:b=4:5

a:b=3:5

a:b=2:5

a:b=1:4

a:b=1:3

a:b=5:7

Find Three Numbers

Find Six Numbers

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Category	Comment	Link	Annotated text
word problem/find a number	perfect number	ספר_דיני_ממונות#x3Is	109) If you want to find the second [perfect number] קט)‫MS L: om. ואם תרצה למצא השני
word problem/find a number	perfect number	ספר_דיני_ממונות#IXt8	108) 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 number	perfect number	ספר_דיני_ממונות#CaJp	110) If you want to find the third [perfect number] קי)‫MS L: om. ואם ואם תרצה למצא השלישי

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