Xavier bought bottles of persimmon syrup, dragonfruit syrup and guava syrup of 300 mℓ, 200 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, dragonfruit syrup and guava 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 200: 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 200
Factors of 250: 1, 2, 5, 10, 25, 50, 125, 250
Highest common factor of 300 mℓ, 200 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
= 300 ÷ 50
= 6
Number of cups of dragonfruit syrup
= 200 ÷ 50
= 4
Number of cups of guava syrup
= 250 ÷ 50
= 5
Xavier would have 6 cups of persimmon syrup, 4 cups of dragonfruit syrup, 5 cups of guava syrup
Answer(s): (a) 50 mℓ; (b) 6, 4, 5