Difference between revisions of "Find a Number Problems"

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Revision as of 17:55, 2 November 2022

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\bmod1=0;a\bmod2=1;a\bmod3=2;a\bmod4=3;a\bmod5=4;a\bmod6=5;a\bmod7=1


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


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


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


[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}


[Expand]repeated subtraction

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}

Three Proportional Numbers

[Expand]three proportional numbers

Four Proportional Numbers

[Expand]four proportional numbers

Five Proportional Numbers

[Expand]five proportional numbers

Six Proportional Numbers

[Expand]six proportional numbers

Seven Proportional Numbers

[Expand]seven proportional numbers

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