Warren bought bottles of passion fruit syrup, lemon syrup and guava syrup of 500 mℓ, 400 mℓ and 450 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, lemon syrup and guava 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 400: 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 200, 400
Factors of 450: 1, 2, 3, 5, 6, 9, 10, 15, 18, 25, 30, 45, 50, 75, 90, 150, 225, 450

Highest common factor of 500 mℓ, 400 mℓ and 450 mℓ = 50 mℓ

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

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

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

Number of cups of guava syrup
= 450 ÷ 50
= 9

Warren would have 10 cups of passion fruit syrup, 8 cups of lemon syrup, 9 cups of guava syrup

Answer(s): (a) 50 mℓ; (b) 10, 8, 9