A plumber bought some pieces of copper and plastic pipe. Each piece of copper pipe was 1 metre long and each piece of plastic pipe was 5 metres long. He bought 35 pieces of pipe. The total length of the pipe was 99 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 1 metre long and each piece of plastic pipe was 5 metres long. He bought 35 pieces of pipe. The total length of the pipe was 99 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 = 35 (since the total number of pipes is 35)
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C1 + P5 = 99 (since the total length of the pipes is 99 metres)
We can solve these equations step by step:
Step 1: From equation 1, we can express P in terms of C: P = 35 - C
Step 2: Substitute P from step 1 into equation 2: C*1 + (35 - C)*5 = 99
Step 3: Simplify the equation from step 2: C + 175 - 5C = 99
Step 4: Rearrange the equation from step 3 to find C: 4C = 76
Step 5: Solve for C: C = 76 / 4 = 19
Step 6: Substitute C = 19 into equation 1 to find P: 19 + P = 35, so P = 35 - 19 = 16
So, the plumber bought 19 pieces of copper pipe and 16 pieces of plastic pipe.
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