SOLUTION: A crew consists of 1 apprentice, 1 journeyman, and 1 master carpenter. The crew receives a check for $5100 for a job they finished. A journeyman makes 300% of what an apprentice ma

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: A crew consists of 1 apprentice, 1 journeyman, and 1 master carpenter. The crew receives a check for $5100 for a job they finished. A journeyman makes 300% of what an apprentice ma      Log On


   

Question 475944: A crew consists of 1 apprentice, 1 journeyman, and 1 master carpenter. The crew receives a check for $5100 for a job they finished. A journeyman makes 300% of what an apprentice makes and a master carpenter makes make 150% of what a journeyman makes. How much does each person on the crew earn?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let a = apprentices earnings
Let j = journeyman's earnings
Let m = master carpenter's earnings
given:
(1) +a+%2B+j+%2B+m+=+5100+
(2) +j+=+3a+
(3) +m+=+1.5j+
This is 3 equations and 3 unknowns,
so it's solvable
-------------------
(2) +j+=+3a+
(2) +a+=+j%2F3+
Substitute (2) and (3) into (1)
(1) +a+%2B+j+%2B+m+=+5100+
(1) +j%2F3+%2B+j+%2B+1.5j+=+5100+
Multiply both sides by 3
(1) +j+%2B+3j+%2B+4.5j+=+15300+
(1) +8.5j+=+15300+
(1) +j+=+1800+
and,
(2) +a+=+j%2F3+
(2) +a+=+600+
and,
(3) +m+=+1.5j+
(3) +m+=+1.5%2A1800+
(3) +m+=+2700+
$600 = apprentices earnings
$1800 = journeyman's earnings
$2700 = master carpenter's earnings
check:
+600+%2B+1800+%2B+2700+=+5100+
+5100+=+5100+
OK