In England, mass is measured in units called stones. One pound equals 1/14 of a stone. A cat weighs 3/4 stone. How many pounds d

oes the cat weigh?

Mathematics

1 answer:

allsm [11]2 years ago

7 0

$\bf \begin{array}{ccll}
stones&lbs\\
\text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\
\frac{1}{14}&1\\\\
\frac{3}{4}&p
\end{array}\implies \cfrac{\quad \frac{1}{14}\quad }{\frac{3}{4}}=\cfrac{1}{p}\implies \cfrac{1}{14}\cdot \cfrac{4}{3}=\cfrac{1}{p}
\\\\\\
 \cfrac{2}{21}=\cfrac{1}{p}\implies p=\cfrac{21\cdot 1}{2}\implies p=\cfrac{21}{2}\implies p=10\frac{1}{2}$

You might be interested in

Please help me!!!!!!!

hammer [34]

Answer:no

Step-by-step explanation:

3 0

3 years ago

At a school with 100? students, 33 were taking? Arabic, 32 ?Bulgarian, and 40 Chinese. 9 students take only? Arabic, 12 take onl

Stels [109]

Answer: The answer is 4 and 32.

Step-by-step explanation: Let "A", "B" and "C" represents the set of students who were taking Arabic, Bulgarian and Chinese respectively.

The, according to the given information, we have

$n(A)=33,~~n(B)=32,~~n(C)=40,~~n(A\cap B)=14.$

Let 'p' represents the number of students who take all the three languages, then

$n(A\cap B\cap C)=p.$

Also,

$n(A)-n(A\cap B)-n(A\cap C)+n(A\cap B\cap C)=9\\\\\Rightarrow n(A\cap B)+n(A\cap C)=24+p~~~~~~~~~~~~~~(a),\\\\n(A\cap B)+n(B\cap C)=20+p~~~~~~~~~~~~~~(b),\\\\n(B\cap C)+n(A\cap C)=20+p~~~~~~~~~~~~~~~(c).$

From here, we get after subtracting equation(c) from (b) that

$n(A\cap B)=n(A\cap C)=14.$

Therefore,

$p=14+14-24=4,$ and from equation (a), we find

$n(B\cap C)=24-14=10.$

Thus,

$n(A\cap B\cap C)=4$ and

$n(A\cup B\cup C)=n(A)+n(B)+n(C)-n(A\cap B)-n(B\cap C)-n(A\cap C)+n(A\cap B\cap C)\\\\\Rightarrow n(A\cap B\cap C)=33+32+40-9-12-20+4\\\\\Rightarrow n(A\cap B\cap C)=68.$