in what ratio must two sorts of sugar costing $390 and $315 be mixed in order to produce a mixture worth $69 per kg?

2 answers

no way can you mix two expensive items to produce a cheap mixture.
Also, you have not specified the cost per kg of either of the two sugars.
let the highest prime number that can go into 390 and 315 represent the number of sugar for each set.
the highest prime is 5
390/5=#78 per kg for this set
also, 315/5=#63 per kg for this set
for each sale of #78 per kg, loss = (78-69)=#9
for each sale of #63 per kg, gain= (69-63)#6
hence, ratio will be 9:6 = 3:2
check
6×78=468
9×63=567
567+468=1035
similarly; 69×15=1035.