Daniel bought bottles of mangosteen syrup, persimmon syrup and mango syrup of 350 mℓ, 200 mℓ and 300 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 mangosteen syrup, persimmon syrup and mango 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 200: 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 200
Factors of 300: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 150, 300

Highest common factor of 350 mℓ, 200 mℓ and 300 mℓ = 50 mℓ

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

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

Number of cups of persimmon syrup
= 200 ÷ 50
= 4

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

Daniel would have 7 cups of mangosteen syrup, 4 cups of persimmon syrup, 6 cups of mango syrup

Answer(s): (a) 50 mℓ; (b) 7, 4, 6