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== Three Proportional Numbers==
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Revision as of 19:05, 21 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#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 a Perfect Number

[Expand]perfect number

Find One Number

[Expand]\scriptstyle\frac{7a}{9}=49


[Expand]\scriptstyle\frac{a}{5}\sdot8=23


[Expand]\scriptstyle\frac{\frac{1}{5}a}{\sqrt{a}}=7


[Expand]\scriptstyle\frac{3}{a}=5+\frac{7}{b}


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


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


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


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


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


[Expand]\scriptstyle a+\left(\frac{1}{3}\sdot a\right)+\left(\frac{2}{5}\sdot a\right)=81


[Expand]\scriptstyle a-\left(\frac{1}{3}\sdot a\right)-\left(\frac{1}{4}\sdot a\right)=29


[Expand]\scriptstyle\left(\frac{1}{2}a+\frac{1}{3}a\right)-\left(\frac{1}{4}a+\frac{1}{5}a\right)=4


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


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


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


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


[Expand]\scriptstyle\frac{2}{5}a^2=a


[Expand]\scriptstyle a+28=2a^2


[Expand]\scriptstyle a^2\sdot a=12a+10a^2


[Expand]\scriptstyle\sqrt{9a}=12


[Expand]\scriptstyle\sqrt{a}+\sqrt{a-\sqrt{a}}=3


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


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


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


[Expand]\scriptstyle\frac{1}{4}\sdot a=\frac{1}{3}\left[a-\left(\frac{1}{4}\sdot a\right)\right]=\frac{1}{2}\sdot\left[\left[a-\left(\frac{1}{4}\sdot a\right)\right]-\frac{1}{3}\left[a-\left(\frac{1}{4}\sdot a\right)\right]\right]


[Expand]\scriptstyle\frac{3a}{4}:4=4:6


[Expand]\scriptstyle2:3=4:a


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


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


[Expand]\scriptstyle\frac{4a}{5}=6+\frac{3}{5}


[Expand]\scriptstyle4a\bmod5=1


[Expand]\scriptstyle4a\bmod6=1


[Expand]\scriptstyle a\bmod3=a\bmod5=a\bmod7=1


[Expand]\scriptstyle a\bmod3=2;a\bmod5=4;a\bmod7=6


[Expand]\scriptstyle a^2+19=b^2


[Expand]\scriptstyle a^2-15=b^2


[Expand]\scriptstyle\begin{cases}\scriptstyle a+4=n^2\\\scriptstyle a-4=m^2\end{cases}


[Expand]\scriptstyle\begin{cases}\scriptstyle a^2-5a=n^2\\\scriptstyle a^2+7a=m^2\end{cases}


Find Two Numbers

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


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


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


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


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

b=2a

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

a:b=2:3

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


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


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


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


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


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


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


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


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


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


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


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


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


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


[Expand]\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}


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


a:b=3:4

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


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


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


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


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


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


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


a:b=4:5

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


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

a:b=3:5

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


[Expand]\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}


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


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


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


a:b=2:5

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


a:b=1:4

[Expand]\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

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


a:b=5:7

[Expand]\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

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

[Expand]\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}

[Expand]\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}

[Expand]\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}

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

[Expand]\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}

[Expand]\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}

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

Three Proportional Numbers

[Expand]three proportional numbers

Four Proportional Numbers

[Expand]four proportional numbers

Five Proportional Numbers

[Expand]five proportional numbers

Find Six Numbers

[Expand]six proportional numbers

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