Ben bought bottles of persimmon syrup, chikoo syrup and mangosteen syrup of 300 mℓ, 450 mℓ and 350 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, chikoo syrup and mangosteen 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 450: 1, 2, 3, 5, 6, 9, 10, 15, 18, 25, 30, 45, 50, 75, 90, 150, 225, 450
Factors of 350: 1, 2, 5, 7, 10, 14, 25, 35, 50, 70, 175, 350
Highest common factor of 300 mℓ, 450 mℓ and 350 mℓ = 50 mℓ
So, 50 mℓ is the largest possible amount of syrup in each cup.
(b)
Number of cups of persimmon syrup
= 300 ÷ 50
= 6
Number of cups of chikoo syrup
= 450 ÷ 50
= 9
Number of cups of mangosteen syrup
= 350 ÷ 50
= 7
Ben would have 6 cups of persimmon syrup, 9 cups of chikoo syrup, 7 cups of mangosteen syrup
Answer(s): (a) 50 mℓ; (b) 6, 9, 7