What are the possible values of x and y when d equals 58x plus 145y and that d is the HCF of 58 and 145 showing work?

Answer 1

If d is the highest common factor of 58 and 145 then d equals 29:-

So: 29 = 58x+145y

Divide all terms by 29: 1 = 2x+5y

Or: 2*1/4+5*1/10 = 1

Therefore the possible values of x and y are 1/4 and 1/10 respectively

Check: 58*1/4 plus 145*1/10 = 29