Paul bought bottles of mangosteen syrup, kiwi syrup and dragonfruit syrup of 500 mℓ, 300 mℓ and 200 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 mangosteen syrup, kiwi syrup and dragonfruit 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 300: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 150, 300
Factors of 200: 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 200
Highest common factor of 500 mℓ, 300 mℓ and 200 mℓ = 100 mℓ
So, 100 mℓ is the largest possible amount of syrup in each cup.
(b)
Number of cups of mangosteen syrup
= 500 ÷ 100
= 5
Number of cups of kiwi syrup
= 300 ÷ 100
= 3
Number of cups of dragonfruit syrup
= 200 ÷ 100
= 2
Paul would have 5 cups of mangosteen syrup, 3 cups of kiwi syrup, 2 cups of dragonfruit syrup
Answer(s): (a) 100 mℓ; (b) 5, 3, 2