Let \( p \) be the price of Chandler's phone. Since Alec's phone was 20% more expensive than Chandler's, the price of Alec's phone can be expressed as:
\[ p + 0.2p = 1.2p \]
Chandler's total expense is the price of his phone plus the cost of the warranty and the phone case:
\[ p + 37 + 55 = p + 92 \]
Alec's total expense is the price of his phone along with the same warranty and phone case costs:
\[ 1.2p + 37 + 55 = 1.2p + 92 \]
Since both friends spent the same amount of money, we can set up the equation:
\[ p + 92 = 1.2p + 92 \]
To solve for \( p \), we can simplify the equation by subtracting \( 92 \) from both sides:
\[ p = 1.2p \]
If we simplify this, we get:
\[ 0 = 0.2p \]
From this, we see that we can derive:
\[ 0.2p = 0 \]
Correcting this, we need to set the equations correctly for comparison. The better equation to start with is:
\[ p + 92 = 1.2p + 92 \]
Subtract \( 92 \) from both sides:
\[ p = 1.2p \]
Now subtract \( p \) from both sides:
\[ 0 = 0.2p \]
We can cancel that out and shift the equation:
\[ 92 = 0.2p \]
Now solve for \( p \):
\[ p = \frac{92}{0.2} = 460 \]
So the price of Chandler's phone is:
\[ \boxed{460} \]
Therefore, the price of Chandler's phone is $460.