Sixty more than nine times a number is the same as two less than ten times the number. What is the number?

Full solution

Q. Sixty more than nine times a number is the same as two less than ten times the number. What is the number?

Set Up Equation: Let's denote the unknown number as ' $x$ '. According to the problem, sixty more than nine times the number ( $9x + 60$ ) is the same as two less than ten times the number ( $10x - 2$ ). We can set up the following equation to represent this relationship: $\newline$ $9x + 60 = 10x - 2$
Solve for x: Now, we need to solve for 'x'. Let's move all terms involving 'x' to one side and constant terms to the other side. We can subtract $9x$ from both sides to get: $\newline$ $9x + 60 - 9x = 10x - 2 - 9x$ $\newline$ This simplifies to: $\newline$ $60 = x - 2$
Isolate x: Next, we add $2$ to both sides to isolate 'x': $\newline$ $60 + 2 = x - 2 + 2$ $\newline$ This gives us: $\newline$ $62 = x$
Check Solution: We have found the value of $x$ . To ensure there are no math errors, we can substitute $x$ back into the original equation to check if both sides are equal: $\newline$ $9x + 60 = 10x - 2$ $\newline$ $9(62) + 60 = 10(62) - 2$ $\newline$ $558 + 60 = 620 - 2$ $\newline$ $618 = 618$ $\newline$ Since both sides are equal, our solution is correct.