Tommy bought bottles of mangosteen syrup, dragonfruit syrup and guava syrup of 400 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 mangosteen syrup, dragonfruit syrup and guava syrup would he have respectively? Give your answers in numbers (Eg 1, 2, 3)

(a)
Factors of 400: 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 200, 400
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 400 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 mangosteen syrup
= 400 ÷ 50
= 8

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

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

Tommy would have 8 cups of mangosteen syrup, 7 cups of dragonfruit syrup, 4 cups of guava syrup

Answer(s): (a) 50 mℓ; (b) 8, 7, 4