Mark bought bottles of mango syrup, guava syrup and pear 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 mango syrup, guava syrup and pear 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 mango syrup
= 250 ÷ 50
= 5

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

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

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

Answer(s): (a) 50 mℓ; (b) 5, 8, 4