Topic : Age Word Problem
Question : When Juan divides each of five consecutive integers by his age, the sum of the five remainders he gets is 32. when nicki, who is several years older divides each of a diferrent set of five consecutive integrs by her age, the sum of the five remainders is also 32. what is the sum of the ages of juan and nicki?
Answer :
The answer I got is
1)First person,s Age16----- consecutive integers 14,15,16, 17,18 remainders are 14, 15, 0, 1,2 total 32
2)Second person’s Age27----- consecutive integers are 26,27,28,29,30
Remainders are 26, 0, 1, 2, 3 total 32
sum of the ages= 43
Method I had adopted
Remainders can be
r, r+1, r+2, r+3,r+4, total 32= 5r+10 implies r is not an integer , hence ruled out.
r, r+1,r+2, r+3,0 total32= 4r+ 6 implies r is not an integer ruled out
r, r+1, r+2, 0,1 total 32 = 3r+4implies r= not an integer
r,r+1,0, 1,2 total 32= 2r +4 r= 14 implies possibility
r,0, 1,2,3 total 32= r+6 , r= 26 possible
0,r,r+1,r+2, r+3, total 32= 4r+ 6 implies r not an integer
Case1 r=14
This implies remainders 14,15,0,1,2 -------total 32 consecutive integers are 14,15,16,17,18
Evidently 16 meets the requirement. That is the age of person1 is 16
Case2 r= 26,0,1,2,3, consecutive integers are 26,27,28,29,30
Evidently 27 meets the requirement,Age of second person is 27
Hope the Entire Explanation did the needful.
Question : When Juan divides each of five consecutive integers by his age, the sum of the five remainders he gets is 32. when nicki, who is several years older divides each of a diferrent set of five consecutive integrs by her age, the sum of the five remainders is also 32. what is the sum of the ages of juan and nicki?
Answer :
The answer I got is
1)First person,s Age16----- consecutive integers 14,15,16, 17,18 remainders are 14, 15, 0, 1,2 total 32
2)Second person’s Age27----- consecutive integers are 26,27,28,29,30
Remainders are 26, 0, 1, 2, 3 total 32
sum of the ages= 43
Method I had adopted
Remainders can be
r, r+1, r+2, r+3,r+4, total 32= 5r+10 implies r is not an integer , hence ruled out.
r, r+1,r+2, r+3,0 total32= 4r+ 6 implies r is not an integer ruled out
r, r+1, r+2, 0,1 total 32 = 3r+4implies r= not an integer
r,r+1,0, 1,2 total 32= 2r +4 r= 14 implies possibility
r,0, 1,2,3 total 32= r+6 , r= 26 possible
0,r,r+1,r+2, r+3, total 32= 4r+ 6 implies r not an integer
Case1 r=14
This implies remainders 14,15,0,1,2 -------total 32 consecutive integers are 14,15,16,17,18
Evidently 16 meets the requirement. That is the age of person1 is 16
Case2 r= 26,0,1,2,3, consecutive integers are 26,27,28,29,30
Evidently 27 meets the requirement,Age of second person is 27
Hope the Entire Explanation did the needful.
