Xavier bought bottles of persimmon syrup, mangosteen syrup and guava syrup of 350 mℓ, 200 mℓ and 400 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 persimmon syrup, mangosteen syrup and guava 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 200: 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 200
Factors of 400: 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 200, 400

Highest common factor of 350 mℓ, 200 mℓ and 400 mℓ = 50 mℓ

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

(b)
Number of cups of persimmon syrup
= 350 ÷ 50
= 7

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

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

Xavier would have 7 cups of persimmon syrup, 4 cups of mangosteen syrup, 8 cups of guava syrup

Answer(s): (a) 50 mℓ; (b) 7, 4, 8