Cody bought bottles of pomegranate syrup, grapefruit syrup and mangosteen syrup of 150 mℓ, 500 mℓ and 350 mℓ respectively. He counted to pour them into smaller cups of equal amount with no leftover.
- What was the largest possible amount of syrup in each cup?
- How many cups of syrup of pomegranate syrup, grapefruit syrup and mangosteen syrup would he have respectively? Give your answers in numbers (Eg 1, 2, 3)
(a)
Factors of 150: 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, 150
Factors of 500: 1, 2, 4, 5, 10, 20, 25, 50, 100, 125, 250, 500
Factors of 350: 1, 2, 5, 7, 10, 14, 25, 35, 50, 70, 175, 350
Highest common factor of 150 mℓ, 500 mℓ and 350 mℓ = 50 mℓ
So, 50 mℓ is the largest possible amount of syrup in each cup.
(b)
Number of cups of pomegranate syrup
= 150 ÷ 50
= 3
Number of cups of grapefruit syrup
= 500 ÷ 50
= 10
Number of cups of mangosteen syrup
= 350 ÷ 50
= 7
Cody would have 3 cups of pomegranate syrup, 10 cups of grapefruit syrup, 7 cups of mangosteen syrup
Answer(s): (a) 50 mℓ; (b) 3, 10, 7