Question

Hayden says:
'If I multiply my number by 2 and subtract 5 then multiply the result by 6, the answer is 5 less than 167'
What number was Hayden first thinking of?

Answer 1

Let Hayden's number be represented by \( x \).

According to Hayden's statement, the process he follows can be expressed mathematically as follows:

1. Multiply the number by 2: \( 2x \)
2. Subtract 5: \( 2x - 5 \)
3. Multiply the result by 6: \( 6(2x - 5) \)

This result is stated to be 5 less than 167. Therefore, we can set up the equation:

\[
6(2x - 5) = 167 - 5
\]

This simplifies to:

\[
6(2x - 5) = 162
\]

Now, let's solve for \( x \):

1. Distributing the 6:
\[
12x - 30 = 162
\]

2. Adding 30 to both sides:
\[
12x = 162 + 30
\]
\[
12x = 192
\]

3. Dividing both sides by 12:
\[
x = \frac{192}{12} = 16
\]

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