Vanessa purchased a bottle of grapefruit syrup to make drinks. She used ¹₃ of the syrup in April. She then used the remaining syrup in May and June in the ratio 1 : 8. Given that the amount of the grapefruit syrup used in April was 0.77 ℓ more than that in May, how many millilitres of grapefruit syrup did the bottle contain at first?

April	May	June	Total
1x9	2x9		3x9
	1x2	8x2
9 u	2 u	16 u	27 u

Total volume of May and June is combined repeated identity.  Make the total volume of May and June the same.  LCM of 2 and 9 is 18.

Volume of more grapefruit syrup in the bottle used in April than May
= 9 u - 2 u
= 7 u

7 u = 0.77 

1 u = 0.77 ÷ 7 = 0.11

Amount of grapefruit syrup in the bottle at first
= 27 u
= 27 x 0.11
= 2.97 ℓ

1 ℓ = 1000 mℓ

Amount of grapefruit syrup in the bottle at first
= 2.97 x 1000
= 2970 mℓ

Answer(s): 2970 mℓ