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# Word Problems/Math

Question
Hi Abe,i will love to get your view on this plz as you are a math expert. I have been give a portfolio of \$11 millions to collect on while my co-workers have been given a portfolio of \$ 6 millions each. Our monthly goal is the average % of the total portfolio collected by each team member. If X ,Y and Z collect \$300,000 this correspond to 5% of their portfolio, if i collect the same amount it equals to 2.7%....since there are 4 of us in the team then the average % collected for the team is 4.43%...and i am way below the team average and when I complained that this is not fair since i felt that i had to work twice harder to be able to catch up to these fellas, i was told that mathematically it was fair because i had opportunity to collect more since my portfolio was larger and it did not mean that i had to work harder. Can you please confirm whether this statement is true? Mathematically is it possible to prove that i am not at a disadvantage? Thanks for answering.

Hello Patricia,

Mathematically, it is true -- based on percentages.  But I suspect that there is more to this
than simple percentages.  Is the expected return directly proportional to the amounts you have
to invest?  For example, let's say you have twice as much to invest than others (which is
approximately true), does that mean it is reasonable to expect you get a return that is twice
as much (or more)?  I am not a finance/investment expert, so I do not know if that is reasonable
or not.  In my novice opinion, isn't it generally true the more you have to invest, the more
opportunities and greater flexibility one has?  Anyhow, from a purely mathematical view (percentages),
I'd agree with the expectation, but do not know if it is ultimately fair since I do not fully
understand the mechanisms in place for investments.

I hope this helps.

Abe M.

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Word Problems

Volunteer

#### Abe Mantell

##### Expertise

Hello, I am a college professor of mathematics and regularly teach all levels from elementary mathematics through differential equations, and would be happy to assist anyone with such questions!

##### Experience

Over 15 years teaching at the college level.

Organizations
NCTM, NYSMATYC, AMATYC, MAA, NYSUT, AFT.

Education/Credentials
B.S. in Mathematics from Rensselaer Polytechnic Institute
M.S. (and A.B.D.) in Applied Mathematics from SUNY @ Stony Brook