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x/2+y/3=17
3x+2y=102 (Ec. 1)
Un tercio del primero (x/3), un medio del segundo (y/2), entonces:
x/3+y/2=18
2x+3y=108 (Ec. 2)
Por igualación, despejamos x en ambas:
(102-2y)/3=(108-3y)/2
2(102-2y)=3(108-3y)
204-4y=324-9y
5y=324-204
y=120/5=24
Sustituimos y=24:
x=(102-2y)/3
x=(102-2(24))/3
x=(102-48)/3
x=18