Henry bought bottles of pomegranate syrup, passion fruit syrup and chikoo syrup of 200 mℓ, 350 mℓ and 400 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 pomegranate syrup, passion fruit syrup and chikoo 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 350: 1, 2, 5, 7, 10, 14, 25, 35, 50, 70, 175, 350
Factors of 400: 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 200, 400

Highest common factor of 200 mℓ, 350 mℓ and 400 mℓ = 50 mℓ

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

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

Number of cups of passion fruit syrup
= 350 ÷ 50
= 7

Number of cups of chikoo syrup
= 400 ÷ 50
= 8

Henry would have 4 cups of pomegranate syrup, 7 cups of passion fruit syrup, 8 cups of chikoo syrup

Answer(s): (a) 50 mℓ; (b) 4, 7, 8