Question

Twice the sum of a number and 9 is equal to three times the difference of the number and 9 Find the number.

Answer 1

45

Explanation:

You want the number described by, "twice the sum of a number and 9 is equal to three times the difference of the number and 9."

Setup

Let x represent the number. Then "twice the sum of the number and 9" is ...

2(x +9)

and "three times the difference of the number and 9" is ...

3(x -9)

These are equal, so we have ...

2(x +9) = 3(x -9)

Solution

Eliminating parentheses gives ...

2x +18 = 3x -27

45 = x . . . . . . . . . . . add 27-2x

The number is 45.