# Thread: Problem solving question for fish - not sure if this is algebra but need help!

1. ## Problem solving question for fish - not sure if this is algebra but need help!

Hi everyone,

I am wondering if someone can help me out with a problem I need to solve. I'm not sure if this is the right forum for the question, so if it isn't - it would also REALLY be helpful if you could point me in the right direction for help with this. This isn't for a school or Uni course, it is for a fisheries research project I am involved with.

I am essentially looking for a formula to use on excel that could help me do the following - I know I might have to look at an excel help forum for this but as I don't even understand the math I thought it best to start here:

In a year, Irish recreational fishermen went fishing for a total of 701 900 days. The maximum amount of fish caught on any one of these days was 731.7778 kg, the minimum amount was 0 kg. No days were the same amount of fish caught and the amount of fish caught on any day differed from another by the exactly same amount of fish. So - on first of the 701 900 days 0 fish were caught, on the next a tiny bit more, the next a tiny bit more than the day before that... continuing to the 701 900th day where 731.7778 kg of fish were caught. I need to find out the total amount of fish caught summed over all 701 900 days. So, imagine an excel file with the following two columns:

Day Amount caught (kg)
1 0
2 731.7778/701900
3 2 X (731.7778/701900)
4 3 X (731.7778/701900)
5 4 X (731.7778/701900)
.
.
701900 701899 X (731.7778/701900)
TOTAL SUM OF ALL CAUGHT ON ALL DAYS????

Again, it would be most helpful if someone could tell me how I could (easily - without having to create 701900 rows) calculate this total in excel (the formula). I will likely have to do this numerous times in future, so to have an tiny short explanation and description of the formula would be wicked - or a point in the right direction to somewhere where I could possibly get help with this. Thank you so so so so much!!

Best,
Dana

2. ## Re: Problem solving question for fish - not sure if this is algebra but need help!

Hi everyone,

I am wondering if someone can help me out with a problem I need to solve. I'm not sure if this is the right forum for the question, so if it isn't - it would also REALLY be helpful if you could point me in the right direction for help with this. This isn't for a school or Uni course, it is for a fisheries research project I am involved with.

I am essentially looking for a formula to use on excel that could help me do the following - I know I might have to look at an excel help forum for this but as I don't even understand the math I thought it best to start here:

In a year, Irish recreational fishermen went fishing for a total of 701 900 days. The maximum amount of fish caught on any one of these days was 731.7778 kg, the minimum amount was 0 kg. No days were the same amount of fish caught and the amount of fish caught on any day differed from another by the exactly same amount of fish. So - on first of the 701 900 days 0 fish were caught, on the next a tiny bit more, the next a tiny bit more than the day before that... continuing to the 701 900th day where 731.7778 kg of fish were caught. I need to find out the total amount of fish caught summed over all 701 900 days. So, imagine an excel file with the following two columns:

Day Amount caught (kg)
1 0
2 731.7778/701900
3 2 X (731.7778/701900)
4 3 X (731.7778/701900)
5 4 X (731.7778/701900)
.
.
701900 701899 X (731.7778/701900)
TOTAL SUM OF ALL CAUGHT ON ALL DAYS????

Again, it would be most helpful if someone could tell me how I could (easily - without having to create 701900 rows) calculate this total in excel (the formula). I will likely have to do this numerous times in future, so to have an tiny short explanation and description of the formula would be wicked - or a point in the right direction to somewhere where I could possibly get help with this. Thank you so so so so much!!

Best,
Dana
1. Let $\displaystyle \displaystyle{q = \frac{731.7778}{701900}}$

2. Then you want to determine:

$\displaystyle \displaystyle{0 \cdot q + 1\cdot q+2\cdot q+3\cdot q+ ...+701900\cdot q}$

Factor out q:

$\displaystyle \displaystyle{q(0+1+2+3+...+701900)}$

3. In parantheses you find the sum of an arithmetic sequence:

$\displaystyle \displaystyle{0+1+2+3+...+n = \frac n2(n-1)}$

4. Use this formula to get the total amount of fish:

$\displaystyle \displystyle{A(fish)=\frac{731.7778}{701900}\left( \frac{701900}2 \cdot(701900-1) \right)}$