$$\frac{150(3)+112.5(2)+150(m)+120(4)}{3+2+m+4}=127\cdot5$$
$m = -\frac{912}{97} = -9\frac{39}{97} \approx -9.402061856$
$$150\times 3+112.5\times 2+150m+120\times 4=127\times 5\left(m+9\right)$$
$$450+112.5\times 2+150m+480=127\times 5\left(m+9\right)$$
$$450+225+150m+480=127\times 5\left(m+9\right)$$
$$675+150m+480=127\times 5\left(m+9\right)$$
$$1155+150m=127\times 5\left(m+9\right)$$
$$1155+150m=635\left(m+9\right)$$
$$1155+150m=635m+5715$$
$$1155+150m-635m=5715$$
$$1155-485m=5715$$
$$-485m=5715-1155$$
$$-485m=4560$$
$$m=\frac{4560}{-485}$$
$$m=-\frac{912}{97}$$
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