A student cuts 1/3 of a coil of wire. He then cuts out another piece that was 8 meters long (I assume from the remaining coil). The two pieces of cut off wire are only half the total length of the wire. How long was the coil before the student cut it? I am getting 25, 50, to 150m but my equation doesn't match each time I check. Thank you for your help.

We know that after cutting 1/3 of the coil and 8m of the coil, 1/2 of the coil remains. This can be written as 1/3 + x = 1/2, where x will be 1/6. We know that this 1/6 of the coil is 8m, so the total length of the coil is 8 * 6 = 48m because one coil = 6 subcoils each of 8m.

To solve this problem, let's break it down step by step.

Let's assume the total length of the coil before cutting was x meters.

The student first cuts off 1/3 of the coil, which leaves (2/3)x meters of wire remaining.

Then the student cuts out another piece that is 8 meters long from the remaining wire. This means that (2/3)x - 8 meters of wire is left.

According to the given information, the sum of the two cut-off pieces is half the total length of the wire. So we can set up the following equation:

1/3x + 8 = 1/2x

Now let's solve this equation step by step:

Multiply every term by 6 to eliminate the denominators:
6 * 1/3x + 6 * 8 = 6 * 1/2x

2x + 48 = 3x

Subtract 2x from both sides:
2x - 2x + 48 = 3x - 2x

48 = x

Therefore, the total length of the coil before cutting was 48 meters.

I hope this explanation helps you understand how to solve the problem.