Question 737364
m = mother's age this year.
n = some unknown whole number.
i = some unknown whole number, i<>n.

m=5*n
m-1=3*i
m<50 and m>25, or 25<m<50


The axioms are not seeming to help.  Using the inequality for m and the requirement of m is multiple of 5, the possibilities are m is an element of {30, 35, 40, 45}.


Last year mother was m-1, which was specified as a multiple of 3.  30-1=29, which will not fit because it's not a multiple of 3.  m-1 is an element of {33, 36, 39, 42, 45, 48 }.  We must adjust this set for m-1+1, so that m-1+1=m which must be an element of {34, 37, 40, 43, 46, 49}.


We now have two sets for the possible values of m, and m can ONLY be one of those values.  We want the INTERSECTION of the two sets, {30, 35, 40, 45} with {34, 37, 40, 43, 46, 49}.  What element is in BOTH sets?  {{{highlight(40)}}}.

m=40 this year.  Mother is 40 years of age this year.