Zane bought bottles of persimmon syrup, mango syrup and pomegranate syrup of 450 mℓ, 300 mℓ and 250 mℓ respectively. He counted to pour them into smaller cups of equal amount with no leftover.
- What was the largest possible amount of syrup in each cup?
- How many cups of syrup of persimmon syrup, mango syrup and pomegranate syrup would he have respectively? Give your answers in numbers (Eg 1, 2, 3)
(a)
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
Factors of 250: 1, 2, 5, 10, 25, 50, 125, 250
Highest common factor of 450 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 persimmon syrup
= 450 ÷ 50
= 9
Number of cups of mango syrup
= 300 ÷ 50
= 6
Number of cups of pomegranate syrup
= 250 ÷ 50
= 5
Zane would have 9 cups of persimmon syrup, 6 cups of mango syrup, 5 cups of pomegranate syrup
Answer(s): (a) 50 mℓ; (b) 9, 6, 5