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I really wondered about it...

In my text book, there are examples about how to use past perfect tense. Like :

I had eaten the cake before I went to sleep.

He has done his work and went to play computer games.

And then today when I was reading my book, I saw an example is like :

Until the new software was purchased, the staff had struggled to keep the accounts records up to date.

In the above example, "was purchased" this possible past perfect tense is followed by "had struggled" this past perfect tense. My teacher taught me that we use past perfect tense to state something which happened firstly and past tense to something that happened after. So I thought the last example should have used "is purchased" this past tense instead of "was purchased" this past perfect, am I right?
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Hi,
loveCZUntil the new software was purchased, the staff had struggled to keep the accounts records up to date.

In the above example, "was purchased" this possible past perfect tense is followed by "had struggled" this past perfect tense. My teacher taught me that we use past perfect tense to state something which happened firstly and past tense to something that happened after. So I thought the last example should have used "is purchased" this past tense instead of "was purchased" this past perfect, am I right?
First thing first, let's give the verb forms their correct names. Emotion: smile

was purchased >> past simple, passive
had struggled>> past perfect
is purchased>> present simple, passive

The time sequence in your example sentence is something like this:
1. in the past, the staff had struggled to keep the accounts record up to date
2. so (in a less remote past) the firm (or company, or whatever) purchased a new software
3. as a result, the staff does not struggle any more.

So, the tenses are fine: the struggling (which is in past perfect: 'had struggled') happened before the purchasing (which is in simple past: 'was purchased') of the software. This agrees with your teacher's explanation, right?
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Oh Right! Now I understand more about tenses. Had + pp = Past Perfect, or else like "was done","was brought","was born" are also simple past,am I right?

Thanks so much
Hi
loveCZHad + pp = Past Perfect
loveCZ "was done","was brought","was born" are simple past
Both correct. Emotion: smile

Until the new software was purchased [by someone], the staff has struggled to keep the account record up to day.

Was purchased = indirect speed not past perfect in this case.

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