Question 737364: mother's age this year is multiple of 5. last year her age was a multiple of 3. she is lessthan 50years and morethan 25years. what is her age?
Answer by josgarithmetic(39617)   (Show Source):
You can put this solution on YOUR website! 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
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?  .
m=40 this year. Mother is 40 years of age this year.
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