Hi again!

36 and 44 do add up to 80, which fulfills one of the equations given: \( a-b = 80 \). Now, let's see if it satisfies the other equation, \( \frac{a+b}{2} = 180\). There are two possible cases:

\( a = 180+36 = 216 \) and \( b = 180-44 = 136 \)
\( a = 180+44 = 224 \) and \( b = 180-36 = 144 \)

(We are only adding numbers to \( a \) because it must be greater than \( b \).)

For the first case, the average (\( \frac{a+b}{2} \)) would be:

\( \frac{216+136}{2} = \frac{352}{2} = 176 \)

For the second case, the average would be:

\( \frac{224+144}{2} = \frac{368}{2} = 184 \)

Hence, when we use 36 and 44, it does not satisfy \( \frac{a+b}{2} = 180\). In fact, this is true for all pairs of numbers other than 36 and 44. I hope this helps!

Happy Learning,

The Daily Challenge Team