Seth bought bottles of orange syrup, grapefruit syrup and kiwi syrup of 200 mℓ, 250 mℓ and 150 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, grapefruit syrup and kiwi syrup would he have respectively? Give your answers in numbers (Eg 1, 2, 3)

(a)
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
Factors of 150: 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, 150

Highest common factor of 200 mℓ, 250 mℓ and 150 mℓ = 50 mℓ

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

(b)
Number of cups of orange syrup
= 200 ÷ 50
= 4

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

Number of cups of kiwi syrup
= 150 ÷ 50
= 3

Seth would have 4 cups of orange syrup, 5 cups of grapefruit syrup, 3 cups of kiwi syrup

Answer(s): (a) 50 mℓ; (b) 4, 5, 3