Question

Carter says:
'I decided to add 4 to my number then multiply the result by 3, After that I subtracted 5 then doubled the result. The answer is 110'
What number was Carter first thinking of?

Answer 1

Let's denote the number Carter was first thinking of as \( x \).

According to Carter's process:
1. He added 4 to his number: \( x + 4 \)
2. Then he multiplied the result by 3: \( 3(x + 4) \)
3. After that, he subtracted 5: \( 3(x + 4) - 5 \)
4. Finally, he doubled the result: \( 2(3(x + 4) - 5) \)

We know that the final result is 110, so we can set up the following equation:

\[
2(3(x + 4) - 5) = 110
\]

Now, let's solve this step by step.

1. Divide both sides by 2:

\[
3(x + 4) - 5 = 55
\]

2. Add 5 to both sides:

\[
3(x + 4) = 60
\]

3. Divide both sides by 3:

\[
x + 4 = 20
\]

4. Subtract 4 from both sides:

\[
x = 16
\]

Thus, the number Carter was first thinking of is \( \boxed{16} \).