Word Problem Involving Number of Workers

Smith industries has 50 workers. Yellow workers are paid $600 per week and red workers are paid $1000 per week. Smith industries weekly payroll is $42,000. How many red workers does Smith industries have? 

y = number of yellow workers
50 - y = number of red workers {there are 50 total workers employed} 

600y + 1000(50 - y) = 42,000 {number of workers times price of worker equals total payout}
600y + 50,000 - 1000y = 42,000 {used distributive property}
-400y + 50,000 = 42,000 {combined like terms}
-400y = -8,000 {subtracted 50,000 from each side}
y = 20 {divided each side by -400}
50 - y = 30 {substituted 20, in for y, into 50 - y} 

there are 30 red workers {50 - y represented red workers}


- Algebra House