Asher bought bottles of starfruit syrup, dragonfruit syrup and grapefruit syrup of 350 mℓ, 300 mℓ and 250 mℓ respectively. He counted to pour them into smaller cups of equal amount with no leftover.

1. What was the largest possible amount of syrup in each cup?
2. How many cups of syrup of starfruit syrup, dragonfruit syrup and grapefruit syrup would he have respectively? Give your answers in numbers (Eg 1, 2, 3)

(a)
Factors of 350: 1, 2, 5, 7, 10, 14, 25, 35, 50, 70, 175, 350
Factors of 300: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 150, 300
Factors of 250: 1, 2, 5, 10, 25, 50, 125, 250

Highest common factor of 350 mℓ, 300 mℓ and 250 mℓ = 50 mℓ

So, 50 mℓ is the largest possible amount of syrup in each cup.

(b)
Number of cups of starfruit syrup
= 350 ÷ 50
= 7

Number of cups of dragonfruit syrup
= 300 ÷ 50
= 6

Number of cups of grapefruit syrup
= 250 ÷ 50
= 5

Asher would have 7 cups of starfruit syrup, 6 cups of dragonfruit syrup, 5 cups of grapefruit syrup

Answer(s): (a) 50 mℓ; (b) 7, 6, 5