Ivan bought bottles of passion fruit syrup, kiwi syrup and grapefruit syrup of 350 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 passion fruit syrup, kiwi syrup and grapefruit syrup would he have respectively? Give your answers in numbers (Eg 1, 2, 3)

(a)
Factors of 350: 1, 2, 5, 7, 10, 14, 25, 35, 50, 70, 175, 350
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 350 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 passion fruit syrup
= 350 ÷ 50
= 7

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

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

Ivan would have 7 cups of passion fruit syrup, 3 cups of kiwi syrup, 4 cups of grapefruit syrup

Answer(s): (a) 50 mℓ; (b) 7, 3, 4