Question

3 friends pay \[pounds18\] each to hire a hall for a band practice. How much would 9 friends pay each to hire the same hall?

Answer 1

Hint: Here in this question, we have to find the how much money paid by each when 9 friends hire the hall. In the question they mentioned the same hall then the cost of the hall will never change when it was 3 or 9 friends. To solve this the price of hall is divided by the number of friends i.e., 9 to get the amount which is paid by each one.

Complete step by step answer:
Consider the given question:
 The 3 friends paid \[pounds18\] each to hire the hall. To get the total cost, we have to multiply the number of friends by the amount of money each friend paid:
i.e., \[3 \times pounds18 = pounds54\]
Therefore, the cost to hire the hall is \[pounds54\],
Thus, \[n\left( x \right) = 54\]--------(1)
Where, \[n\] being the number of friends and \[x\] being the amount each friend pays towards the total cost.
Now, we have to find out how much money is paid by each when 9 friends hire the same hall.
When, hiring the same hall the cost will remains same i.e., \[pounds54\]
Consider the equation (1)
\[ \Rightarrow \,\,\,n\left( x \right) = 54\]
When 9 friends hire the hall, the value of n is 9 i.e., \[n = 9\], then
\[ \Rightarrow \,\,\,9\left( x \right) = 54\]
Divide both side by 9
\[ \Rightarrow \,\,\,\dfrac{{9\left( x \right)}}{9} = \dfrac{{54}}{9}\]
On simplification, we get
\[ \Rightarrow \,\,\,x = 6\]

Hence, each friend in the group of 9 friends pays \[pounds\,6\] to hire the hall.

Note: The problem is related to the simple arithmetic operations. the problem is related to the word problem, we should read the question u have to group the given data and then by using the simple arithmetic operations like addition, subtraction, multiplication and the division we solve the question.