Carl's hands trembled as he stood in front of the safe and unfolded the crumpled piece of paper holding the combination that would open the safe. "Rats!' he moaned. The combination was written in the form of a riddle. The last number was described in the following way: Find 2/3 of the final number, add 16, and this number will b e equal to two times the myster number. What was the final number of the combination? Explain in detail how you found you answer.

do you mean the number e? or is that just an extra e?

if that's just an extra e then i believe it goes something like this.
First you set up the equation.
(2/3)the final number x, +16 is equal to 2 times the mystery number x.

so, (2/3)x +16 = 2x

first you subtract 16 from both sides, then times both sides by (2/3) reciprocal, (3/2). Then you will have x=3x-24.

subtract 3x from both sides and you will get -2x=-24. Divide by two.

The extra e is a mystery.

12

To solve the equation (2/3)x + 16 = 2x, we can follow these steps:

Step 1: Subtract 16 from both sides of the equation:

(2/3)x + 16 - 16 = 2x - 16

(2/3)x = 2x - 16

Step 2: Multiply both sides of the equation by the reciprocal of (2/3), which is 3/2:

(3/2) * (2/3)x = (3/2) * (2x - 16)

x = (3/2) * 2x - (3/2) * 16

x = 3x - 24

Step 3: Subtract 3x from both sides of the equation:

x - 3x = -24

-2x = -24

Step 4: Divide both sides of the equation by -2:

(-2x) / -2 = -24 / -2

x = 12

Therefore, the final number of the combination is 12.

To find the answer, let's solve the equation step by step:

1. The equation we have is (2/3)x + 16 = 2x, where x represents the final number of the combination.

2. Start by subtracting 16 from both sides of the equation to isolate the x term:

(2/3)x + 16 - 16 = 2x - 16

Simplifying, we get (2/3)x = 2x - 16.

3. Next, we need to eliminate the fraction. Multiply every term by the reciprocal of the fraction, which is 3/2:

(3/2)(2/3)x = (3/2)(2x - 16)

Simplifying, we have (1)x = 3x - 24.

4. Now, subtract 3x from both sides to isolate the x term:

x - 3x = -24

Simplifying, we get -2x = -24.

5. To solve for x, divide both sides of the equation by -2:

(-2x) / (-2) = (-24) / (-2)

Simplifying, we have x = 12.

Therefore, the final number of the combination is 12.