Reggie bought bottles of starfruit syrup, lemon syrup and grapefruit syrup of 150 mℓ, 450 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 starfruit syrup, lemon syrup and grapefruit syrup would he have respectively? Give your answers in numbers (Eg 1, 2, 3)
(a)
Factors of 150: 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, 150
Factors of 450: 1, 2, 3, 5, 6, 9, 10, 15, 18, 25, 30, 45, 50, 75, 90, 150, 225, 450
Factors of 200: 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 200
Highest common factor of 150 mℓ, 450 mℓ and 200 mℓ = 50 mℓ
So, 50 mℓ is the largest possible amount of syrup in each cup.
(b)
Number of cups of starfruit syrup
= 150 ÷ 50
= 3
Number of cups of lemon syrup
= 450 ÷ 50
= 9
Number of cups of grapefruit syrup
= 200 ÷ 50
= 4
Reggie would have 3 cups of starfruit syrup, 9 cups of lemon syrup, 4 cups of grapefruit syrup
Answer(s): (a) 50 mℓ; (b) 3, 9, 4