Wesley bought bottles of pomegranate syrup, mango syrup and kiwi syrup of 250 mℓ, 450 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 pomegranate syrup, mango syrup and kiwi syrup would he have respectively? Give your answers in numbers (Eg 1, 2, 3)

(a)
Factors of 250: 1, 2, 5, 10, 25, 50, 125, 250
Factors of 450: 1, 2, 3, 5, 6, 9, 10, 15, 18, 25, 30, 45, 50, 75, 90, 150, 225, 450
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 250 mℓ, 450 mℓ and 300 mℓ = 50 mℓ

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

(b)
Number of cups of pomegranate syrup
= 250 ÷ 50
= 5

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

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

Wesley would have 5 cups of pomegranate syrup, 9 cups of mango syrup, 6 cups of kiwi syrup

Answer(s): (a) 50 mℓ; (b) 5, 9, 6