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The Oddville Academy offers three languages: Oriya, Dakhini, and Dutch (how odd!). Each student takes an odd number of languages – that is, every student takes either one language or three languages.

Let  be the number of students taking Oriya,  be the number of students taking Dakhini,  be the number of students taking Dutch, and  be the number of students taking all three languages. Find an expression in terms of  and  for the total number of students at the Oddville Academy.

Feb 25, 2018

#1
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o = students taking Oriya

d =                          Dakhini

h =                           Dutch

t  =                           all three

Since you are either taking   o d or h     or you are taking all three   t

If you are  t   you are counted in o and d and h  (the same amount)

so we will subtract them from EACH of the  o d and h   and then add the t

the total number of students   = o-t  + d-t + h-t   + t

Total students = o + d + h  - 3t + t

Total students = o + d + h - 2t

Feb 25, 2018
#2
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But why do you add t at the end?

Feb 25, 2018
#3
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t is number of students taking all 3 languages ....we subtraced them from the single language classes so we have to count them at the end.

ElectricPavlov  Feb 25, 2018