Archie bought bottles of persimmon syrup, mango syrup and mangosteen syrup of 500 mℓ, 450 mℓ and 150 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 persimmon syrup, mango syrup and mangosteen syrup would he have respectively? Give your answers in numbers (Eg 1, 2, 3)

(a)
Factors of 500: 1, 2, 4, 5, 10, 20, 25, 50, 100, 125, 250, 500
Factors of 450: 1, 2, 3, 5, 6, 9, 10, 15, 18, 25, 30, 45, 50, 75, 90, 150, 225, 450
Factors of 150: 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, 150

Highest common factor of 500 mℓ, 450 mℓ and 150 mℓ = 50 mℓ

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

(b)
Number of cups of persimmon syrup
= 500 ÷ 50
= 10

Number of cups of mango syrup
= 450 ÷ 50
= 9

Number of cups of mangosteen syrup
= 150 ÷ 50
= 3

Archie would have 10 cups of persimmon syrup, 9 cups of mango syrup, 3 cups of mangosteen syrup

Answer(s): (a) 50 mℓ; (b) 10, 9, 3