Carl bought bottles of apple syrup, persimmon syrup and starfruit syrup of 250 mℓ, 450 mℓ and 300 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 apple syrup, persimmon syrup and starfruit 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 apple syrup
= 250 ÷ 50
= 5
Number of cups of persimmon syrup
= 450 ÷ 50
= 9
Number of cups of starfruit syrup
= 300 ÷ 50
= 6
Carl would have 5 cups of apple syrup, 9 cups of persimmon syrup, 6 cups of starfruit syrup
Answer(s): (a) 50 mℓ; (b) 5, 9, 6