Can someone help me with a math (fraction) question?

Pocket10s

Pocket10s

Pocket10s

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Joined
4 Oct 2014
Posts
517
Hi,

This is probably really stupid; but its really annoying me after my wife asked me (I am the worst at math).

Question:

On a day where all premier league teams kick off at the same time, 3/5 of the goals in the first half were scored by teams in the top 6. In the second half the teams outside the top 6 scored 13/20 of the goals.

What fraction of the total goals did the top 6 teams score?
 
touch said:
edit: that wasn't right. checking again....
Click to expand...

Seemed right to me.

25 goals in total

3/5 were the top teams in the first half
7/20 were the top teams in the second half

10/25, or 2/5, or 40% of goals were scored by the top teams
 
krooton said:
Seemed right to me.

25 goals in total

3/5 were the top teams in the first half
7/20 were the top teams in the second half

10/25, or 2/5, or 40% of goals were scored by the top teams
Click to expand...

I dont think that's how you add fractions.
3/5 + 7/10 is not 10/25

I think @Sui is right with 19/40
 
touch said:
I dont think that's how you add fractions.
3/5 + 7/10 is not 10/25
Click to expand...

I would agree if we were given a 'total goal' amount, but we aren't, so I can only infer that 5 goals were scored in the first halves, and 20 in the second halves.

If there was a different total goal amount, you would need to do the lowest common denominator thing to get the overall fraction.

EDIT: Or

3/5 = 12/20
divided by 2 (because half)
=
6/20
+
3.5/20
=
9.5/20 of goals scored by the top team, or 19/40
 
Last edited:
krooton said:
divided by 2 (because half)
Click to expand...

This is where I'm getting stuck. You can't just divide by 2 because there can be a different number of goals in each half.

Testing some different scenarios, 19/40 doesnt work in most cases.
 
Without knowing the ratio of first half goals to second half goals, you can't answer this question.

Take an extreme example, say zero first half goals are scored, and 20 second half goals are scored. Therefore the top 6 teams scored 7/20 of all goals.

Take the reverse with 5 in the first half and zero in the second half, and top 6 teams scored 3/5 of all goals.

Both are possible events and give different answers. Therefore the number of goals scored in each half (or at least the ratio between them) is needed to answer the question.
 
Last edited:
misread the question :p

Depending on the distribution of goals between first and second half, the answer is somewhere between 0.35 and 0.6
 
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