Let the number of orders that were delivered on time be \(a\).

\(3.5a - 4.3(210-a) = 532.2\)

\(3.5a-903+4.3a=532.2\)

\(7.8a-903=532.2\)

\(7.8a=1435.2\)

\(a=184\)

Now we should check our answers:

If \(184\) orders were delivered on time, Peter would have

\(184\times$3.5=$644\).

If there were \(184\) orders that were on time, there were

\(210-184=26\) late orders.

We should now subtract

\(26\times$4.3=$111.8\)

from Peter's \($644\).

\($644-$111.8=$532.2\)

\(184 \) orders were delivered on time.