Divide a Number Problems

30 into 4 parts

Category	Comment	Link	Annotated text
word problem/divide a number	30 into 4 parts	ספר_דיני_ממונות#7fd8	232) Question: make me four parts out of 30, such that the ratio of the fourth to the third is as the third to the second and as the second to the first. רלב) שאלה תעשה לי מל' ד' חלקים שיהיה יחס הד' אל הג' כג' לב' וכב' לא‫'

Divide Ten into Two Parts

$\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle a^2=4\sdot\left(a\sdot b\right)\end{cases}$

no such category found: #divide 10 into two parts

$\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle a^2=\left(1+\frac{1}{2}\right)\sdot\left(a\sdot b\right)\end{cases}$

no such category found: #divide 10 into two parts

$\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle 10^2=16\sdot a^2\end{cases}$

no such category found: #divide 10 into two parts

$\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle 10^2=\left(6+\frac{1}{4}\right)\sdot a^2\end{cases}$

no such category found: #divide 10 into two parts

$\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\frac{b}{a}=5\end{cases}$

no such category found: #divide 10 into two parts

$\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\frac{b}{a}=4\end{cases}$

no such category found: #divide 10 into two parts

$\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle a^2=9b\end{cases}$

no such category found: #divide 10 into two parts

$\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle a\sdot b=21\end{cases}$

no such category found: #divide 10 into two parts

$\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\frac{a}{b}+\frac{b}{a}=2+\frac{1}{6}\end{cases}$

no such category found: #divide 10 into two parts

$\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\frac{a}{b}-\frac{b}{a}=3+\frac{3}{4}\end{cases}$

no such category found: #divide 10 into two parts

$\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle b^2-a^2=50\end{cases}$

no such category found: #divide 10 into two parts

$\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle a^2=\frac{1}{4}b\end{cases}$

no such category found: #divide 10 into two parts

$\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\left(a-b\right)^2=20+\frac{1}{4}\end{cases}$

no such category found: #divide 10 into two parts

$\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\left(b-a\right)^2-a^2=32\end{cases}$

no such category found: #divide 10 into two parts

$\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle3a=b\sdot\sqrt{8}\end{cases}$

no such category found: #divide 10 into two parts

$\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\left(a-b\right)^2\sdot a=\left(20+\frac{1}{4}\right)a\end{cases}$

no such category found: #divide 10 into two parts

$\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\left(a-b\right)^2\sdot b=\left(20+\frac{1}{4}\right)b\end{cases}$

no such category found: #divide 10 into two parts

$\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\left(a\sdot b\right)\sdot a=21a\end{cases}$

no such category found: #divide 10 into two parts

$\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\left(a-b\right)^2\sdot\left(7+\frac{1}{9}\right)=\left(a\sdot b\right)^2\end{cases}$

no such category found: #divide 10 into two parts

$\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\left[\left(a\sdot b\right)+a^2\right]\sdot a=\left[a\sdot\left(\frac{1}{2}\sdot a\right)\right]^2+36\end{cases}$

no such category found: #divide 10 into two parts

$\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle b^2-a^2=80\end{cases}$

no such category found: #divide 10 into two parts

$\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\frac{a}{b}+\frac{b}{a}=4+\frac{1}{4}\end{cases}$

no such category found: #divide 10 into two parts

$\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\frac{a}{b}-\frac{b}{a}=\frac{5}{6}\end{cases}$

no such category found: #divide 10 into two parts

$\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\frac{a}{b}=4+\frac{1}{4}\end{cases}$

no such category found: #divide 10 into two parts

$\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle6a+\frac{1}{3}\sdot\frac{6a}{b}=56\end{cases}$

no such category found: #divide 10 into two parts

$\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\frac{b}{a}+a=5+\frac{1}{2}\end{cases}$

no such category found: #divide 10 into two parts

$\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\left(\frac{b}{a}+b\right)\sdot a=30\end{cases}$

no such category found: #divide 10 into two parts

$\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\frac{b}{a}\sdot b=9\end{cases}$

no such category found: #divide 10 into two parts

$\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\left(\frac{b}{a}\right)^2\sdot a=32\end{cases}$

no such category found: #divide 10 into two parts

$\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\frac{b}{a}\sdot\left(b-a\right)=24\end{cases}$

no such category found: #divide 10 into two parts

$\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\left(\frac{a}{b}+\frac{b}{a}\right)\sdot b=34\end{cases}$

no such category found: #divide 10 into two parts

$\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\left(\frac{b}{a}+10\right)\sdot a=46\end{cases}$

no such category found: #divide 10 into two parts

$\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\left(\frac{b}{a}+10\right)\sdot b=69\end{cases}$

no such category found: #divide 10 into two parts

$\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\left(\frac{a}{b}+\frac{b}{a}+10\right)\sdot a=73\end{cases}$

no such category found: #divide 10 into two parts

$\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\left(\frac{a}{b}-\frac{b}{a}\right)\sdot a=5\end{cases}$

no such category found: #divide 10 into two parts

$\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\left(\frac{a}{b}+\frac{b}{a}\right)\sdot a=25-2a\end{cases}$

no such category found: #divide 10 into two parts

$\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\left(\frac{a}{b}+a\right)\sdot\left(\frac{b}{a}+b\right)=35\end{cases}$

no such category found: #divide 10 into two parts

$\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\left(\frac{b}{a}+10\right)\sdot\left(\frac{a}{b}+10\right)=122+\frac{2}{3}\end{cases}$

no such category found: #divide 10 into two parts

$\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\left(\frac{b}{a}+10\right)\sdot\left(10-\frac{a}{b}\right)=107+\frac{{\color{red}{1}}}{3}\end{cases}$

no such category found: #divide 10 into two parts

$\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\frac{a\sdot b}{b-a}=\sqrt{6}\end{cases}$

no such category found: #divide 10 into two parts

$\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle b^2-\left(a\sdot\sqrt{8}\right)=40\end{cases}$

no such category found: #divide 10 into two parts

$\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle a\sdot\sqrt{10}=b^2\end{cases}$

no such category found: #divide 10 into two parts

$\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\frac{a}{b}+\frac{b}{a}=\sqrt{5}\end{cases}$

no such category found: #divide 10 into two parts

$\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\left(\frac{a}{b}\right)^2+\left(\frac{b}{a}\right)^2=3\end{cases}$

no such category found: #divide 10 into two parts

$\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\frac{b}{a}-\frac{a}{b}=\frac{5}{6}\end{cases}$

no such category found: #divide 10 into two parts

$\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\left(\frac{b}{a}\right)^2-\left(\frac{a}{b}\right)^2=2\end{cases}$

no such category found: #divide 10 into two parts

$\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle a+2\sqrt{a}=b-2\sqrt{b}\end{cases}$

no such category found: #divide 10 into two parts

$\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\frac{10}{a}+\frac{10}{b}=6+\frac{1}{4}\end{cases}$

no such category found: #divide 10 into two parts

$\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\frac{10}{a}\sdot\frac{10}{b}=6+\frac{1}{4}\end{cases}$

no such category found: #divide 10 into two parts

$\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\frac{40}{a}\sdot\frac{40}{b}=100\end{cases}$

no such category found: #divide 10 into two parts

$\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\frac{50}{a}\sdot\frac{40}{b}=125\end{cases}$

no such category found: #divide 10 into two parts

$\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\left({\color{red}{\frac{10}{a}\sdot\frac{10}{b}}}\right)^2=20+\frac{1}{4}\end{cases}$

no such category found: #divide 10 into two parts

$\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\left(\frac{40}{a}\right)^2+\left(\frac{40}{b}\right)^2=625\end{cases}$

no such category found: #divide 10 into two parts

Divide Thirty into Two Parts

$\scriptstyle\begin{cases}\scriptstyle a+b=30\\\scriptstyle\frac{a}{b}=27\end{cases}$

Category	Comment	Link	Annotated text
word problem/divide a number	a+b=30;a/b=27	מלאכת_המספר#RDUf	Example: as we took 5 as the quotient for 10, we take 27 as the quotient for thirty. המשל כי כמו שלקחנו לחלק ה' מי' נקח לחלק כ"ז משלשים

Divide Ten into Three Parts

$\scriptstyle\begin{cases}\scriptstyle a+b+c=10\\\scriptstyle a^2+b^2=c^2\\\scriptstyle a\sdot c=b^2\end{cases}$

no such category found: #divide 10 into three parts