Dylan bought bottles of apple syrup, persimmon syrup and lemon syrup of 500 mℓ, 300 mℓ and 250 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 apple syrup, persimmon syrup and lemon syrup would he have respectively? Give your answers in numbers (Eg 1, 2, 3)

(a)
Factors of 500: 1, 2, 4, 5, 10, 20, 25, 50, 100, 125, 250, 500
Factors of 300: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 150, 300
Factors of 250: 1, 2, 5, 10, 25, 50, 125, 250

Highest common factor of 500 mℓ, 300 mℓ and 250 mℓ = 50 mℓ

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

(b)
Number of cups of apple syrup
= 500 ÷ 50
= 10

Number of cups of persimmon syrup
= 300 ÷ 50
= 6

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

Dylan would have 10 cups of apple syrup, 6 cups of persimmon syrup, 5 cups of lemon syrup

Answer(s): (a) 50 mℓ; (b) 10, 6, 5