Perry bought bottles of persimmon syrup, peach syrup and starfruit syrup of 200 mℓ, 250 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 persimmon syrup, peach syrup and starfruit syrup would he have respectively? Give your answers in numbers (Eg 1, 2, 3)

(a)
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
Factors of 350: 1, 2, 5, 7, 10, 14, 25, 35, 50, 70, 175, 350

Highest common factor of 200 mℓ, 250 mℓ and 350 mℓ = 50 mℓ

So, 50 mℓ is the largest possible amount of syrup in each cup.

(b)
Number of cups of persimmon syrup
= 200 ÷ 50
= 4

Number of cups of peach syrup
= 250 ÷ 50
= 5

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

Perry would have 4 cups of persimmon syrup, 5 cups of peach syrup, 7 cups of starfruit syrup

Answer(s): (a) 50 mℓ; (b) 4, 5, 7