Difference between revisions of "Find a Number Problems"
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<div class="mw-collapsible mw-collapsed"><math>\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}</math><div class="mw-collapsible-content"> | <div class="mw-collapsible mw-collapsed"><math>\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}</math><div class="mw-collapsible-content"> | ||
{{#annotask: | {{#annotask: | ||
− | [[category: #a | + | [[category: #find three numbers]] |
+ | [[comment: (a²·a)+b²=12½c]] | ||
+ | }}</div></div><br> | ||
+ | |||
+ | <div class="mw-collapsible mw-collapsed"><math>\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}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
[[comment: (a²·a)+b²=12½c]] | [[comment: (a²·a)+b²=12½c]] | ||
}}</div></div><br> | }}</div></div><br> |
Revision as of 03:51, 1 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?
:![]() |
word problem/find a number | repeated subtraction | ספר_חשבון#QPoG | 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? : ![]() 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
|}
:![]() |
Contents
Find One Number
![\scriptstyle\left(\frac{1}{3}\sdot a\right)+\left(\frac{1}{5}\sdot a\right)=10](/mediawiki/images/math/f/2/8/f28b4c771e77dbc7dcb98af71ef08ff3.png)
Category | Comment | Link | Annotated text |
---|---|---|---|
word problem/find a number | ⅓a+⅕a=10 | מלאכת_המספר#niUj | Suppose we want to find any whole, such that the sum of its third and its fifth together is ten.
:![]() |
![\scriptstyle\left(\frac{1}{3}\sdot a\right)+\left(\frac{1}{4}\sdot a\right)=10+\frac{1}{2}](/mediawiki/images/math/b/d/8/bd822bc67030d7942d3e1cfb0db901a1.png)
Category | Comment | Link | Annotated text |
---|---|---|---|
word problem/find a number | ⅓a+¼a=10½ | מלאכת_המספר#IQCS | Example 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\left(\frac{1}{3}\sdot a\right)+\left(\frac{1}{4}\sdot a\right)=20](/mediawiki/images/math/0/8/0/08094f551584479f1c17dbb3d1d18b9f.png)
Category | Comment | Link | Annotated text |
---|---|---|---|
word problem/find a number | ⅓a+¼a=20 | מלאכת_המספר#Auzt | Example: we wish to find a number that the sum of its third and its quarter is 20.
:![]() |
![\scriptstyle\left(\frac{1}{3}\sdot a\right)+\left(\frac{1}{4}\sdot a\right)=6](/mediawiki/images/math/1/9/2/1928a87a5904f5d3461c7d591e56b417.png)
Category | Comment | Link | Annotated text |
---|---|---|---|
word problem/find a number | ⅓a+¼a=6 | מלאכת_המספר#m65t | Example: we wish to find a number, whose quarter and third are 6.
:![]() |
![\scriptstyle\left(\frac{1}{4}\sdot a\right)+\left(\frac{1}{5}\sdot a\right)=5](/mediawiki/images/math/7/c/d/7cd4fec3e1d27f7ea9230263d2c2e9cd.png)
Category | Comment | Link | Annotated text |
---|---|---|---|
word problem/find a number | ¼a+⅕a=5 | מלאכת_המספר#0Nd6 | As 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 a-\left(\frac{1}{3}\sdot a\right)=\sqrt{a}](/mediawiki/images/math/2/0/a/20a124bcb5fae68b6e897fa4123e9d84.png)
no such category found: #find one number
![\scriptstyle\left[a-\left(\frac{2}{3}\sdot a\right)\right]^2=20](/mediawiki/images/math/0/2/0/020aa7d4628e7b55eaa289ac0c2211b9.png)
no such category found: #find one number
![\scriptstyle\left[a\sdot\left(\frac{2}{3}\sdot a\right)\right]^2=36](/mediawiki/images/math/4/4/d/44d26474e128ec5582fe301dd2b9863a.png)
no such category found: #find one number
![\scriptstyle a^2\sdot\left(\frac{3}{4}\sdot a^2\right)=6a](/mediawiki/images/math/c/b/d/cbde7b868affb4c4fcf47515c524b92f.png)
no such category found: #find one number
![\scriptstyle a+28=2a^2](/mediawiki/images/math/3/d/2/3d235459b8141d0d943317b212700d6e.png)
no such category found: #find one number
![\scriptstyle a^2\sdot a=12a+10a^2](/mediawiki/images/math/b/0/c/b0c5064d33a87bfedcb2acd43935b8ed.png)
no such category found: #find one number
![\scriptstyle\sqrt{9a}=12](/mediawiki/images/math/d/d/b/ddb5a48a6f896cd9dd92b578fb22624b.png)
no such category found: #find one number
![\scriptstyle\left(a\sdot\frac{2}{3}a\right)^2=\sqrt{50}](/mediawiki/images/math/e/d/5/ed5ba9053cb409cb90f315931861a4a9.png)
no such category found: #find one number
![\scriptstyle\left(a\sdot\frac{2}{3}a\right)\sdot a=a\sdot\sqrt{8}](/mediawiki/images/math/9/9/6/99641c77bfb67f5e71d37323e2fa1088.png)
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](/mediawiki/images/math/7/1/e/71ee8f2c1f0de7a36d44cac3f1df7a51.png)
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?
::![]() |
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?
:![]() רצינו לדעת כמה המספר הנעלם |
![\scriptstyle\frac{3a}{4}:4=4:6](/mediawiki/images/math/1/f/e/1fe105554b9076a361750d648be7543a.png)
no such category found: #find one number
![\scriptstyle4=\frac{1}{3}\sdot15\longrightarrow a=\frac{1}{5}\sdot25](/mediawiki/images/math/3/8/e/38e8abb89d7faf637ef91e8554c91546.png)
no such category found: #find one number
Find Two Numbers
![\scriptstyle\begin{cases}\scriptstyle b-1=a+1\\\scriptstyle2\sdot\left(a-1\right)=b+1\end{cases}](/mediawiki/images/math/a/6/0/a609da3bd8cf43bddc889c33ef87d453.png)
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}](/mediawiki/images/math/f/3/b/f3b005310066463fcd73ccfda9dddc32.png)
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}](/mediawiki/images/math/7/2/1/721847e5a1a132e105e96ab798ca752b.png)
no such category found: #find two numbers
![\scriptstyle\begin{cases}\scriptstyle a^2=b-5\\\scriptstyle a^2+b^2=100\end{cases}](/mediawiki/images/math/5/6/d/56d75f95f9bc504b1cc3215aad61ade7.png)
no such category found: #find two numbers
![\scriptstyle\begin{cases}\scriptstyle a^2=2b+8\\\scriptstyle a^2+b^2=80\end{cases}](/mediawiki/images/math/d/d/e/dde7a90463185002415d2f26317f12ef.png)
no such category found: #find two numbers
b=2a
![\scriptstyle\begin{cases}\scriptstyle b=2a\\\scriptstyle a^2\sdot b=9b\end{cases}](/mediawiki/images/math/8/5/6/85668b446f708c721fb7ebe85eb123a8.png)
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}](/mediawiki/images/math/5/7/7/5778e6c9c9a03e0e9b077d6cbe2e9728.png)
no such category found: #find two numbers
![\scriptstyle\begin{cases}\scriptstyle a:b=2:3\\\scriptstyle a\sdot b=\sqrt{12}\end{cases}](/mediawiki/images/math/d/7/c/d7ca4dc452c803831d261f93c1f4341f.png)
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}](/mediawiki/images/math/6/8/9/6894761d5bc23878106c52f97d9c05d0.png)
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}](/mediawiki/images/math/8/4/4/8444590bed44a4b77e15a15ac1771bb5.png)
no such category found: #find two numbers
![\scriptstyle\begin{cases}\scriptstyle a:b=2:3\\\scriptstyle a\sdot\sqrt{a}=2b\end{cases}](/mediawiki/images/math/5/6/2/5621737413f6c80776d5debda11be8fe.png)
no such category found: #find two numbers
![\scriptstyle\begin{cases}\scriptstyle a:b=2:3\\\scriptstyle a\sdot\sqrt{a}=b^2\end{cases}](/mediawiki/images/math/6/3/e/63e3fb72be68e5cdb6fc36b69033ada8.png)
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}](/mediawiki/images/math/2/8/1/2811d329920f0c5cabbf0e024c817cac.png)
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}](/mediawiki/images/math/a/a/7/aa73a6752376a3c5675e17526c77e447.png)
no such category found: #find two numbers
![\scriptstyle\begin{cases}\scriptstyle a:b=2:3\\\scriptstyle5a+7b=16+\sqrt{8}\end{cases}](/mediawiki/images/math/5/a/8/5a8e4d0717e0e01d1f2e11705831f0e4.png)
no such category found: #find two numbers
![\scriptstyle\begin{cases}\scriptstyle a:b=2:3\\\scriptstyle3a+4\sqrt{b}=30\end{cases}](/mediawiki/images/math/7/3/1/7318fd87d27bfe5f22c56345d41e0edb.png)
no such category found: #find two numbers
![\scriptstyle\begin{cases}\scriptstyle a:b=2:3\\\scriptstyle a\sdot b=20+\sqrt{8}\end{cases}](/mediawiki/images/math/6/1/1/6114cc286f48998793fbb76140b41988.png)
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}](/mediawiki/images/math/5/8/d/58d4f66f0bd9dbfce6556b3b435b0250.png)
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}](/mediawiki/images/math/1/8/0/180749163b5bfcfaa842f000a51d1c2c.png)
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}](/mediawiki/images/math/5/e/a/5ea5803806ae421df2397f3ed59d3e4a.png)
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}](/mediawiki/images/math/3/5/8/35817ed94ff69d6a955e6eb14d64f43f.png)
no such category found: #find two numbers
![\scriptstyle\begin{cases}\scriptstyle a:b=2:3\\\scriptstyle3a+4b=\sqrt[3]{216}\end{cases}](/mediawiki/images/math/3/7/c/37c574e931d2b293ce8e7c05872dd409.png)
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}](/mediawiki/images/math/b/9/3/b93caebe1c68a387de8a12345b1b3955.png)
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}](/mediawiki/images/math/2/7/6/27685f6fea424a3ed99b9d301f33821a.png)
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}](/mediawiki/images/math/3/7/7/377e3c672ff5b2a89822b462efb02429.png)
no such category found: #find two numbers
![\scriptstyle\begin{cases}\scriptstyle a:b=3:4\\\scriptstyle8a=6\sqrt{b}\end{cases}](/mediawiki/images/math/1/c/1/1c1a35e09040a4d48e6540bd84f1f575.png)
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}](/mediawiki/images/math/8/3/1/831a088a4aa20e037f5fa260cebeaa8c.png)
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}](/mediawiki/images/math/a/6/c/a6cd4ca032769d86a68ea2ec0c769903.png)
no such category found: #find two numbers
![\scriptstyle\begin{cases}\scriptstyle a:b=3:4\\\scriptstyle\sqrt[3]{2a+3b}=8\end{cases}](/mediawiki/images/math/f/d/f/fdfeea3918f71a57781b72d247caef5c.png)
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}](/mediawiki/images/math/6/3/4/634a686c9eeedf5acc4ba19231836321.png)
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}](/mediawiki/images/math/3/f/7/3f72877c8d9b9c291c2d66bbc484a684.png)
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}](/mediawiki/images/math/8/6/5/8652b433d3e249eac331710d2c99af0b.png)
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}](/mediawiki/images/math/7/1/1/71187e61ee927d7bba48ce232ff213cc.png)
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}](/mediawiki/images/math/b/8/4/b8464138165daf6288a672eca4648875.png)
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}](/mediawiki/images/math/b/f/1/bf1fc2b44ad63868caab3c3bd171de55.png)
no such category found: #find two numbers
![\scriptstyle\begin{cases}\scriptstyle a:b=3:5\\\scriptstyle a\sdot b=\sqrt[3]{729}\end{cases}](/mediawiki/images/math/0/5/a/05a756d12f1bd790b4653042daf26458.png)
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}](/mediawiki/images/math/a/0/8/a08be844f768528a52e3d231acec1a87.png)
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}](/mediawiki/images/math/1/7/1/171ce646462d735ef90bd02638d35efb.png)
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}](/mediawiki/images/math/6/b/6/6b684d922156985988350c4b2a4c248d.png)
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}](/mediawiki/images/math/c/c/8/cc8ed2de66c014e40d7c530f4ab5a724.png)
no such category found: #find two numbers
Find Three Numbers
![\scriptstyle\begin{cases}\scriptstyle a+b=c\\\scriptstyle a+c=100b\end{cases}](/mediawiki/images/math/1/f/4/1f4a6321e22623a35e3b073db3b5b846.png)
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}](/mediawiki/images/math/8/7/e/87e216cbd495971999df253fc23756c8.png)
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}](/mediawiki/images/math/8/7/e/87e216cbd495971999df253fc23756c8.png)
Category | Comment | Link | Annotated text |
---|---|---|---|
word problem/find a number | (a²·a)+b²=12½c | ספר_ג'יבלי_אלמוקבאלא#iH47 | Find me three numbers, such that the first is a part of the second as 2 is of 3, and the second is of the third as 3 is of 4.
:If the first is multiplied by itself, then the product is multiplied by the first number, and the second number is multiplied by itself, when both products are summed together, its yields the same as the product of the third number by 12 and a half.
:![]() והשני יהיה מהשלישי כמו שהוא ג' בד' ותכה הראשון בעצמו ואח"כ יוכה העולה במספר הראשון בעצמו ואח"כ יוכה המספר השני בעצמו וכשיחוברו יחד שתי אלו ההכאות יעשה כמו הכאת המספר השלישי בי"ב וחצי אשאל כמה יבא להיות כל אחד מהמספרים |
![\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}](/mediawiki/images/math/4/7/e/47e43f6b4de8501b95c9279afd93d1ef.png)
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}](/mediawiki/images/math/2/c/4/2c4fd7b452fbaf1d254eb957a16295df.png)
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}](/mediawiki/images/math/4/0/6/406f5b6e6f91072b83acedcccd9a81ad.png)
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}](/mediawiki/images/math/4/8/e/48eabe6d43dc7431838b3f5b2d971229.png)
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}](/mediawiki/images/math/1/4/3/1430ffebcaf77fc3dc91b99bd55d52c8.png)
no such category found: #find three numbers
three proportional numbers, a·b·c=1000
no such category found: #three proportional numbers