Jenson bought bottles of starfruit syrup, passion fruit syrup and mango syrup of 250 mℓ, 400 mℓ and 500 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, passion fruit syrup and mango 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 400: 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 200, 400
Factors of 500: 1, 2, 4, 5, 10, 20, 25, 50, 100, 125, 250, 500

Highest common factor of 250 mℓ, 400 mℓ and 500 mℓ = 50 mℓ

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

(b)
Number of cups of starfruit syrup
= 250 ÷ 50
= 5

Number of cups of passion fruit syrup
= 400 ÷ 50
= 8

Number of cups of mango syrup
= 500 ÷ 50
= 10

Jenson would have 5 cups of starfruit syrup, 8 cups of passion fruit syrup, 10 cups of mango syrup

Answer(s): (a) 50 mℓ; (b) 5, 8, 10