Word problem about two mechanics

Question

Two mechanics worked on a car. One worked 20 hours and the other worked 15 hours. Together they made $3125. What is the rate chaeged per hour by each mechanic if the sum of the two rafes was $170?

Answer 1

R1 + R2 = 170  <--- sum of the rates is 170 where R1 is the rate charged by the first mechanic

                                and R2 is the rate charged by the 2nd mechanic; this is the FIRST equation

 

20*R1 + 15*R2 = 3125  <---- After working 20 and 15 hours respectively, the combined wages totals 3125;

                                               this is the SECOND equation

 

R2  = 170 - r1 <--- solves the first equation for r2

 

20*r1 + 15( 170 - r1) = 3125  <--- substitutes into the second equation

 

20*r1 + 2550 - 15*r1 = 3125 <--- distributive property

 

5* R1 + 2550 = 3125

 

5*r1 = 3125 - 2550

 

5*r1 = 575

 

r1 = 115

 

The first mechanic charges $115 per hour.

The second mechanic charges $170 - 115 = 55.

 

20*115 + 15*55 = 2300 + 825 = 3125 <-- YES! It checks!!! the answers are correct