Question

Natasha thinks of numbers and subtracts \[\dfrac{2}{3}\] from it and multiplies the result by \[9\].The product now which is obtained is \[7\] times the number she thought of. What is the number?

Answer 1

Hint: While solving the above question we will follow each step stated in the statement and will frame equations accordingly and solve for the desired number asked in the problem.

Complete step by step solution:
Let the number thought by Natasha be \[x\]. As per the provided conditions the algebraic equation obtained is
\[(x - \dfrac{2}{3}) \times 9 = 7x\]
This is a linear equation.Now we will solve the obtained equation in order to determine the value of \[x\].
\[9x - \dfrac{{18}}{3} = 7x \\
\Rightarrow 2x = 6 \\
\therefore x = 3 \\ \]
This means that the number which Natasha thought was \[3\].

Additional Information:
Remember there are various categories of equations which means that the number of variables in a problem is equal to the number of equations required for solving the system of equations. These are solved by the use of substitution or elimination methods.

Note: Read the questions very carefully while forming the equation. The equation obtained was a linear equation with one variable (which means the highest power of the variable is one) so one equation is enough for solving this problem. The chances of mistakes are there if addition or subtraction is done from the other number so it is suggested to follow the BODMAS rules wherever it is required.