A cool algebra
There are four unequal, positive integers and such that 3 . It is also true that and is between 175 and 200. What is the value of ?
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1 solution
Notice 3a+3b+5c-d=0--------------(1) & 2a+2b+9c-d=0-----------------(2).So,3a+3b+5c-d=2a+2b+9c-d or a+b-4c=0--------------(3). Now 2*(2)=4a+4b+18c-2d=0---------------(4).Then (1)+(3) implies,4a+4b+c-d=0.------------------(5). So,(4)-(5) implies, d= 17c.From this equation we can find a value of d.Notice,given that,the value of d is between 175 and 200.The only possible value is 187 which is divisible by 17.So, d=17 & c=11.Now replace the value of c towards equation --------------(3).Then,a+b=44.Finally,a+b-c=44-11=33.