John bought bottles of lemon syrup, passion fruit syrup and pear syrup of 450 mℓ, 200 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 lemon syrup, passion fruit syrup and pear syrup would he have respectively? Give your answers in numbers (Eg 1, 2, 3)

(a)
Factors of 450: 1, 2, 3, 5, 6, 9, 10, 15, 18, 25, 30, 45, 50, 75, 90, 150, 225, 450
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

Highest common factor of 450 mℓ, 200 mℓ and 350 mℓ = 50 mℓ

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

(b)
Number of cups of lemon syrup
= 450 ÷ 50
= 9

Number of cups of passion fruit syrup
= 200 ÷ 50
= 4

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

John would have 9 cups of lemon syrup, 4 cups of passion fruit syrup, 7 cups of pear syrup

Answer(s): (a) 50 mℓ; (b) 9, 4, 7