Wesley bought bottles of mangosteen syrup, grapefruit syrup and chikoo syrup of 500 mℓ, 150 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, grapefruit syrup and chikoo 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 150: 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, 150
Factors of 200: 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 200

Highest common factor of 500 mℓ, 150 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
= 500 ÷ 50
= 10

Number of cups of grapefruit syrup
= 150 ÷ 50
= 3

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

Wesley would have 10 cups of mangosteen syrup, 3 cups of grapefruit syrup, 4 cups of chikoo syrup

Answer(s): (a) 50 mℓ; (b) 10, 3, 4