A plumber bought some pieces of copper and plastic pipe. Each piece of copper pipe was 2 metres long and each piece of plastic pipe was 3 metres long. He bought 7 pieces of pipe. The total length of the pipe was 19 metres. How many pieces of each type of pipe did the plumber buy?
Question
A plumber bought some pieces of copper and plastic pipe. Each piece of copper pipe was 2 metres long and each piece of plastic pipe was 3 metres long. He bought 7 pieces of pipe. The total length of the pipe was 19 metres. How many pieces of each type of pipe did the plumber buy?
Solution
Let's denote the number of copper pipes as C and the number of plastic pipes as P.
From the problem, we have two equations:
-
C + P = 7 (since the plumber bought 7 pieces of pipe in total)
-
2C + 3P = 19 (since each copper pipe is 2 metres long and each plastic pipe is 3 metres long, and the total length of the pipe was 19 metres)
We can solve these equations step by step:
First, let's isolate C in the first equation:
C = 7 - P
Now, we substitute C from the first equation into the second equation:
2(7 - P) + 3P = 19 14 - 2P + 3P = 19 P = 19 - 14 = 5
Substitute P = 5 into the first equation:
C = 7 - 5 = 2
So, the plumber bought 2 pieces of copper pipe and 5 pieces of plastic pipe.
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