Basic math question from book

[Akhan]

Hi,

The attached image shows a progress thermometer, it's a question from a foundation math book.

The answers to the questions are given in the book, which are:
a. £21898
b. £22960
c. £17874

answers a and b make sense if on the diagram we consider the figure next to the year as the amount of money raised at the END of that year. Using the same logic for question c, which is now asking for an answer based on a figure from the start of 1991, the amount raised at the beginning of 1991 would be the same as the amount raised at the end of 1990, which is £66600. This would mean that there's still £33400 required to hit the target £100,000. But the answer given (£17874) for question c only works if we consider £82126 as the starting figure for that year. I'm probably missing something very basic here but is the figure against the year the amount raised at the start or at the end of that year?

Thanks.

 

[Otis]

… answers a and b make sense if on the diagram we consider the figure next to the year as the amount of money raised at the END of that year …

Yes, the figures represent a running total of 'yearly' progress. Such progress cannot be measured until the end of each year, so answers (a) and (b) are correct.

… for question c … the amount raised at the beginning of 1991 would be … £66600. This would mean that there's still £33400 required to hit the target £100,000 …

The target is £1,000,000, so I get £933,400.

Answer (c) does not make sense. It seems there's a typo, somewhere.

 

[Akhan]

The target is £1,000,000, so I get £933,400.

Answer (c) does not make sense. It seems there's a typo, somewhere.

There is a typeo in the book, answer c makes sense if the target is £100,000 not 1,000,000.

 

[Dr.Peterson]

It looks to me like there may be two typos: if the goal was 100,000 rather than 1,000,000, and if they meant the end of 1991, then their answer would be correct.

Now take a look at this version of the problem that I found by searching: https://books.google.com/books?id=7LrYDVqTGQ8C&pg=PA9

 

[Akhan]

if they meant the end of 1991, then their answer would be correct.

This is exactly what I'm talking about. The figure next to 1991 is the amount raised at the end of 1991.

 

[Dr.Peterson]

This is exactly what I'm talking about. The figure next to 1991 is the amount raised at the end of 1991.

Yes; and in the online copy I found, they didn't correct the question to say "the end of 1991" instead of "the start of 1991", but did correct the 1,000,000. Not good.

 

[Steven G]

This type of problems shows why I always say that you need to define things clearly. In the case, the left scale (years) is Not defined clearly at all!

 

[Akhan]

Yes; and in the online copy I found, they didn't correct the question to say "the end of 1991" instead of "the start of 1991", but did correct the 1,000,000. Not good.

I searched for the errata but couldn't find it so I have ordered the updated version from the link you provided. Although they haven't fully corrected this question, I'm hoping there will be fewer errors overall!

Thank you for posting the link Dr.Peterson and thank you to all who helped.​

 

[Otis]

… years … Not defined clearly at all!

Why is that? We're told that the scale denotes yearly progress. Is it clear that progress for a particular year is determined at the end of that year? After all, how could one declare on January 1, 1991, the progress made during 1991?

 

[Steven G]

Why is that? We're told that the scale denotes yearly progress. Is it clear that progress for a particular year is determined at the end of that year? After all, how could one declare on January 1, 1991, the progress made during 1991?

I am not convinced by that. I still feel that it can be either way.