Knowing that $z$ students failed, how many men failed the exam, out of 452 students? (A $1892$ coll. alg. problem)
In Tibbets' College Requirements In Algebra, at Ginn&Compagny, $1892$ I find the following sight problem ( assuming this expression means that the problem can be solved by simple inspection) :
Of 452 students who tried the examination last June, $x$ were men, the rest were women. In all, $z$ students failed. How many of the failures were men?
The only information I can derive from what precedes is that :
number of women : $492-x$.
My question : is this problem simply solvable?
Solution 1:
There are four variables – combinations of pass/fail and male/female – but only three equations corresponding to the quantities $452,x,z$, so the problem per se is not solvable.
However, in 1892 college attendance was mostly reserved to men in the United States, so there may have been the implicit assumption that there are no women and the answer would simply be $z$.