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**Hint:**First we have to define what the terms we need to solve the problem are. Since poultry is the kind of chicken that will produce nearly $15472$eggs. And we just need to fit those eggs into the set of pairs so that they can fit into trays. And also, in particular, that in one tray we are able to fit nearly $30$eggs.

We need to find how many eggs of pairs of trays that we need to fit all $15472$eggs.

**Complete step-by-step solution:**

Since as per the given question that we already know, in one tray we are able to fit exactly $30$eggs.

Now we need to find the total number of trays that can fit all $15472$eggs, so we just divide the total number of eggs into the eggs that fit $30$eggs in a tray. Thus, we are able to find the total number of needed trays.

We can use the formula of division, so we already have the dividend $15472$ eggs and divisor $30$ eggs in a tray and hence a division is the number that divides another number but either completely we can find the whole number or with a Remainder also in the fraction, hence \[\dfrac{\text{Dividend}}{\text{Divisor}} = \text{Quotient}\]

Thus, by division formula we get $\dfrac{{15472}}{{30}} = 515.733$ approximately and we can convert that into $516$

**Hence, we need approximately $516$trays to fit all $15472$ eggs that poultry has produced.**

**Note:**Since we are also able to solve this problem by assuming $x$ as the needed trays for all $15472$ eggs. While means, in one tray we can fit thirty eggs hence we need thirty into times of x;

Thus $30x = 15472 \Rightarrow x = 516$(by cancelling the terms and approximately value)

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