Japheth bought bottles of starfruit syrup, peach syrup and lemon syrup of 150 mℓ, 450 mℓ and 350 mℓ respectively. He counted to pour them into smaller cups of equal amount with no leftover.

1. What was the largest possible amount of syrup in each cup?
2. How many cups of syrup of starfruit syrup, peach syrup and lemon 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 350: 1, 2, 5, 7, 10, 14, 25, 35, 50, 70, 175, 350

Highest common factor of 150 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 starfruit syrup
= 150 ÷ 50
= 3

Number of cups of peach syrup
= 450 ÷ 50
= 9

Number of cups of lemon syrup
= 350 ÷ 50
= 7

Japheth would have 3 cups of starfruit syrup, 9 cups of peach syrup, 7 cups of lemon syrup

Answer(s): (a) 50 mℓ; (b) 3, 9, 7