SOLUTION: One day 4 plumbers and 5 helpers earned $350. At the same rate of pay, another group of 5 plumbers and 6 helpers earned $430. How much does a plumber and how much does a helper ear

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Question 1010739: One day 4 plumbers and 5 helpers earned $350. At the same rate of pay, another group of 5 plumbers and 6 helpers earned $430. How much does a plumber and how much does a helper earn each day? I can not understand these for the life of me.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
This is really the same as: You have 5 oranges and 4 apples
that cost $4 etc. They are just using plumbers and helpers
Let +x+ = daily pay for a plumber
Let +y+ = daily pay for plumber's helper
------------------------------------
(1) +4x+%2B+5y+=+350+
(2) +5x+%2B+6y+=+430+
---------------------
Multiply both sides of (1) by +5+
Multiply both sides of (2) by +4+
Subtract (2) from (1)
(1) +20x+%2B+25y+=+1750+
(2) +-20x+-+24y+=+-1720+
-------------------------
+y+=+30+
and
(1) +4x+%2B+5%2A30+=+350+
(1) +4x+%2B+150+=+350+
(1) +4x+=+200+
(1) +x+=+50+
The daily pay for a plumber is $50
The daily pay for plumber's helper is $30
----------------
check:
(2) +5x+%2B+6y+=+430+
(2) +5%2A50+%2B+6%2A30+=+430+
(2) +250+%2B+180+=+430+
(2) +430+=+430+
OK
You can check equation (1)