Simon bought bottles of pomegranate syrup, pear syrup and peach syrup of 350 mℓ, 400 mℓ and 500 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 pomegranate syrup, pear syrup and peach 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 400: 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 200, 400
Factors of 500: 1, 2, 4, 5, 10, 20, 25, 50, 100, 125, 250, 500

Highest common factor of 350 mℓ, 400 mℓ and 500 mℓ = 50 mℓ

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

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

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

Number of cups of peach syrup
= 500 ÷ 50
= 10

Simon would have 7 cups of pomegranate syrup, 8 cups of pear syrup, 10 cups of peach syrup

Answer(s): (a) 50 mℓ; (b) 7, 8, 10