When a number is multiplied by 2 and 9 is added to the result, the result is 45 more than twice the number…

Question

When a number is multiplied by 2 and 9 is added to the result, the result is 45 more than twice the number. Find the number.

ScanSolve AI Tutor · Accepted Answer

Here's the solution to the problem:

The problem states: "When a number is multiplied by 2 and 9 is added to the result, the result is 45 more than twice the number." Find the number.

Let the unknown number be $y$ .
"A number is multiplied by 2" can be written as $2y$ .
"9 is added to the result" means $2y + 9$ . This is the left side of our equation.
Formulate the right side of the equation.
"Twice the number" is $2y$ .
"45 more than twice the number" means $2y + 45$ . This is the right side of our equation.
Set up the full equation.
$2y + 9 = 2y + 45$
Solve the equation for $y$ .
Subtract $2y$ from both sides of the equation.
$2y - 2y + 9 = 2y - 2y + 45$ $9 = 45$
Analyze the result.
The equation simplifies to $9 = 45$ , which is a false statement. This means there is no value of $y$ that can satisfy the original equation. Therefore, there is no such number that fits the description given in the problem.

The problem statement describes a situation that is mathematically impossible. There is no solution for $y$ .

When a number is multiplied by 2 and 9 is added to the result, the result is 45 more than twice the number. Find the number.