Seth bought bottles of orange syrup, starfruit syrup and mango syrup of 350 mℓ, 200 mℓ and 250 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 orange syrup, starfruit syrup and mango 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 250: 1, 2, 5, 10, 25, 50, 125, 250

Highest common factor of 350 mℓ, 200 mℓ and 250 mℓ = 50 mℓ

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

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

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

Number of cups of mango syrup
= 250 ÷ 50
= 5

Seth would have 7 cups of orange syrup, 4 cups of starfruit syrup, 5 cups of mango syrup

Answer(s): (a) 50 mℓ; (b) 7, 4, 5