Dylan bought bottles of pear syrup, mango syrup and guava syrup of 250 mℓ, 400 mℓ and 200 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 pear syrup, mango syrup and guava syrup would he have respectively? Give your answers in numbers (Eg 1, 2, 3)

(a)
Factors of 250: 1, 2, 5, 10, 25, 50, 125, 250
Factors of 400: 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 200, 400
Factors of 200: 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 200

Highest common factor of 250 mℓ, 400 mℓ and 200 mℓ = 50 mℓ

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

(b)
Number of cups of pear syrup
= 250 ÷ 50
= 5

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

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

Dylan would have 5 cups of pear syrup, 8 cups of mango syrup, 4 cups of guava syrup

Answer(s): (a) 50 mℓ; (b) 5, 8, 4