First brand = A, second brand = B.
A + B = 249ml
9% A + 14% B = 13% 249ml
B = 249ml - A
9% A + 14% (249ml - A) = 13% 249ml
9A + 14 (249ml - A) = 13 * 249ml
9A + 3486ml - 14A = 3237ml
5A = 249ml
A = 49,8ml
B = 249ml - A = 199,2ml
Answer: He should use 49,8ml of first brand and 199,2ml of second brand.
Also note: That's an approximation, because the volumes are not strictly additive. For example: mixing 50ml pure ethanol with 50ml water will give you about 95ml of mixture. To get an accurate answer, you'd have to measure the volume of the final mixture and then divide your total alcohol content by that.
