Gabriel bought bottles of passion fruit syrup, kiwi syrup and dragonfruit syrup of 250 mℓ, 350 mℓ and 200 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 passion fruit syrup, kiwi syrup and dragonfruit 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 350: 1, 2, 5, 7, 10, 14, 25, 35, 50, 70, 175, 350
Factors of 200: 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 200

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

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

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

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

Number of cups of dragonfruit syrup
= 200 ÷ 50
= 4

Gabriel would have 5 cups of passion fruit syrup, 7 cups of kiwi syrup, 4 cups of dragonfruit syrup

Answer(s): (a) 50 mℓ; (b) 5, 7, 4