The answer is 155.53
The cost is $138.25. This is 100%.
The desired markup is 12.5%. Let x be the price after the desired markup. x is 112.5% (100% + 12.5% = 112.5%).
Again:
$138.25 is 100%
x is 112.5%
Make the proportion:
$138.25 : 100% = x : 112.5%
x = $138.25 * 112.5% : 100%
x = $155.53