I don't know how to combine the variables in this problem to arrive at the sum.

Question

Nick and Dave are rewiring a very large house. Nick is a master electrician and can sometimes work alone. Dave is the assistant and only works in a team. Nick makes $150 per day, while Dave makes $30 less. When they finished the job, the total labor cost was $2,190. How many days did each work? (No fractional days.)

Answer 1

Let N = # days Nick worked
Let D = # days Dave worked
 
Nick's money = 150N
Daves money = (150-30)D = 120D
 
150N + 120D = 2190
 
Since Nick can work alone but Dave can't
we know that N must be greater than or
equal to D...  N≥D
 
The answer is N=9, D = 7
 
150(9) + 120(7) = 2190
 
I tried 2 numbers... I set N=10 and it didn't
come out even so I tried N=9 and that
came out correct.