Question

Casey says, "I pick a number, multiply my number by 7, add 18, and my final result is ten times my starting number." What is Casey's starting number?

A. Casey's starting number is 2.
B. Casey's starting number is 4.
C. Casey's starting number is 6.
D. Casey's starting number is 8.

Answer 1

By using algebra, the equation 7x + 18 = 10x is formed, solved by subtracting 7x from both sides and then dividing by 3, yielding the starting number as x = 6.

Step-by-step explanation:

To solve for Casey's starting number, let's use algebra. We'll let x represent the starting number. According to the problem, Casey multiplies this number by 7 and then adds 18 to get a result that is ten times the starting number. So, the equation that represents this situation is:

7x + 18 = 10x

Now, let's solve for x:

1. Subtract 7x from both sides of the equation:
   7x + 18 - 7x = 10x - 7x
   18 = 3x
2. Divide both sides by 3 to solve for x:
   18 / 3 = 3x / 3
   x = 6

Therefore, Casey's starting number is 6, which corresponds to option C.