It's ett antal so that would be ett sammanlagt antal.
If you use it on its own, to mean 'in total', it's an adverb. Sammanlagt är du skyldig mig 120:- 'In total, you owe me SEK120' (example from Wiktionary https://sv.wiktionary.org/wiki/sammanlagt)
We use sammanlagda in the sentence here for the same reason you use total. You could have just said 'the number'; we could have just said antalet.
From the adjective hints:
If the noun is definite, the adjective takes the ending -a in all cases, no matter gender or number. What’s important to note, however, is that whenever a definite noun is used together with an adjective, an article is placed in front of the adjective. This article is den for singular en-words, det for singular ett-words, and de for plural words (note that de is pronounced as ‘dom’).
A whole number in English is synonymous with an integer, i.e. all numbers that can be written with only digits and no fractions, decimals, or other symbols except the minus sign. So it doesn't work as a translation.
Edit: And just for reference, whole number would be heltal in Swedish. :)