Jenson bought bottles of lemon syrup, guava syrup and pomegranate syrup of 400 mℓ, 450 mℓ and 150 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 lemon syrup, guava syrup and pomegranate syrup would he have respectively? Give your answers in numbers (Eg 1, 2, 3)
(a)
Factors of 400: 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 200, 400
Factors of 450: 1, 2, 3, 5, 6, 9, 10, 15, 18, 25, 30, 45, 50, 75, 90, 150, 225, 450
Factors of 150: 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, 150
Highest common factor of 400 mℓ, 450 mℓ and 150 mℓ = 50 mℓ
So, 50 mℓ is the largest possible amount of syrup in each cup.
(b)
Number of cups of lemon syrup
= 400 ÷ 50
= 8
Number of cups of guava syrup
= 450 ÷ 50
= 9
Number of cups of pomegranate syrup
= 150 ÷ 50
= 3
Jenson would have 8 cups of lemon syrup, 9 cups of guava syrup, 3 cups of pomegranate syrup
Answer(s): (a) 50 mℓ; (b) 8, 9, 3