The proportions of gold in three alloys are 40%, 50% and 80% respectively. These alloys are mixed in certain proportions to obtain 30 kg of a new alloy, which has 55% gold. If the amount of the first alloy is 9 kg, what is the amount in kg of the third alloy used?

Let the amount of the second alloy be $x$ kg and the third alloy be $y$ kg.

Since the total weight of the new alloy is 30 kg and the first alloy is 9 kg:

$9 + x + y = 30$

$x + y = 21 \text{ ... (equation 1)}$

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The new alloy has 55% gold. This gold comes from all three alloys combined.

Gold from each alloy is calculated by multiplying its weight with its gold percentage.

Alloy	Weight (kg)	Gold %	Gold amount (kg)
First	9	40%	$9 \times 0.40 = 3.6$
Second	$x$	50%	$x \times 0.50 = 0.5x$
Third	$y$	80%	$y \times 0.80 = 0.8y$
New alloy	30	55%	$30 \times 0.55 = 16.5$

Total gold equation:

$3.6 + 0.5x + 0.8y = 16.5$

$0.5x + 0.8y = 12.9 \text{ ... (equation 2)}$

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From equation 1: $x = 21 - y$

Substituting in equation 2:

$0.5(21 - y) + 0.8y = 12.9$

$10.5 - 0.5y + 0.8y = 12.9$

$10.5 + 0.3y = 12.9$

$0.3y = 2.4$

$y = 8$

The amount of the third alloy is 8 kg.