Help me solve this maths problem

September 14, 2013 6:06 AM

The average length of unemployment in the UK in 2005 was 170 days. For people aged 45 and over, the figure was 220 days. What would the figure be for these aged under 45?
posted by iamsuper to Science & Nature (8 answers total)

I believe that you are missing a piece of information to solve this problem. How many people in the UK, who are unemployed, are under 45? How many people in the UK, who are unemployed, are 45 or over? This proportion of each is necessary to solve the math problem.

(Proportion of total unemployed who are under 45 * length of unemployment, under 45) + (proportion of total unemployed who are over 45 * 220 days) = 170 days

Once you have the two proportions, you can put those in the equation above and solve for "length of unemployment, under 45".
posted by Peter Petridish at 6:13 AM on September 14, 2013 [4 favorites]

You would need to know the total number of people unemployed in each group to be able to answer.
posted by hazyjane at 6:13 AM on September 14, 2013 [1 favorite]

Or on non- preview, what Peter said.
posted by hazyjane at 6:14 AM on September 14, 2013

Response by poster: 30 million working population, 18 million were aged 45 and over. (oops)
posted by iamsuper at 6:19 AM on September 14, 2013

Best answer: 30 million is the total unemployed, and 18 million of those were aged 45 and over? Correct?

If so:

This means that 60% of the total unemployed are 45 or over (18 million divided by 30 million). Therefore, 40% of the total unemployed are under 45. Either a person is under 45 or not, so these proportions add up to 100%.

Back to my previous set up:

(0.4 * length of unemployment, under 45) + (0.6 * 220 days) = 170 days

average length of unemployment, under 45 = 95 days
posted by Peter Petridish at 6:23 AM on September 14, 2013

I can't believe 30M is the unemployed population of the UK. What's the total population? Note that if the given numbers are the total working populations, then the given answer is correct if the unemployment rate over 45 matches the overall rate.
posted by JMOZ at 6:31 AM on September 14, 2013 [2 favorites]

re-read, JMOZ. 30M = total working population. he is still missing req'd info.
posted by FauxScot at 6:38 AM on September 14, 2013

Response by poster: Answer given by Peter Petridish is correct. Numbers are arbitrary and no more info is given in the question.
posted by iamsuper at 6:44 AM on September 14, 2013