Alex worked three job The first job paid 1050hour The second

Alex worked three job. The first job paid $10.50/hour. The second job paid $13/hour. The third job paid $16/hour. In one week Alex worked a total of 54 hours and earned $689. The time he pent at the first job was 10 hours less than the total time he spent at the second and third job. How much time did Alex spend at each job? (For full credit, set up and solve a linear system. clearly label variables you introduce. Write your answer as a sentence.)

Solution

Let, x be hours spent on first job, y be hours spent on second job and z on third job

So,

x+y+z=54

10.5x+13y+16z=689

x=y+z-10 or x-y-z=-10

From first and third equations

2x=44 so x=22

ie 22 hours on first job

SO, y+z=32

10.5x+13y+16z=689

Substituting x=22 gives

13y+16z=458

Solving two equations gives

y=18,z=14