Question 24210
The plumber's rate times the time that he worked gives how much the plumber made.
The apprentice's rate times the time that he worked gives how much the apprentice made.
The total of how much the two made together is $213
Let tp equal the time the plumber worked
Let ta equal the time the apprentice worked

(1) {{{28*tp + 15* ta = 213}}}
The plumber worked 3 more hours than the apprentice, so
{{{tp = ta + 3}}}
rewrite equation (1)
(2)  {{{28*(ta + 3) + 15 * ta = 213}}}
Expand (2)
(3)  {{{28*ta + 84 +15 * ta = 213}}}
Combine terms and subtract 84 from both sides
(4)  {{{43 * ta = 129}}}
(5)  {{{ta = 3}}}
(6)  {{{tp = ta + 3 = 6}}}
substituting ta and tp back into (1),
(7)  {{{28*6 + 15*3 = 213}}}
The plumbers rate times the time he worked = $168
The apprentices rate times the time he worked = $45
$168 + $45 = $213