Lui bought bottles of mango syrup, mangosteen syrup and persimmon syrup of 300 mℓ, 350 mℓ and 500 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 mango syrup, mangosteen syrup and persimmon syrup would he have respectively? Give your answers in numbers (Eg 1, 2, 3)

(a)
Factors of 300: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 150, 300
Factors of 350: 1, 2, 5, 7, 10, 14, 25, 35, 50, 70, 175, 350
Factors of 500: 1, 2, 4, 5, 10, 20, 25, 50, 100, 125, 250, 500

Highest common factor of 300 mℓ, 350 mℓ and 500 mℓ = 50 mℓ

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

(b)
Number of cups of mango syrup
= 300 ÷ 50
= 6

Number of cups of mangosteen syrup
= 350 ÷ 50
= 7

Number of cups of persimmon syrup
= 500 ÷ 50
= 10

Lui would have 6 cups of mango syrup, 7 cups of mangosteen syrup, 10 cups of persimmon syrup

Answer(s): (a) 50 mℓ; (b) 6, 7, 10