Celine had 35kg of pistachios. She sold 3/5 of the pistachios on Saturday and 4/7 of the remaining pistachios on Sunday. She then packed the remaining pistachios into some bags, each containing 5/8 kg of pistachios. (a). How many bags of pistachios did Celine pack at most? (b). What was the mass of pistachios left? Give your answer as a fraction as a fraction in its simplest form.

Celine had 35kg of pistachios. She sold 3/5 of the pistachios on Saturday and 4/7 of the remaining pistachios on Sunday. She then packed the remaining pistachios into some bags, each containing 5/8 kg of pistachios. (a). How many bags of pistachios did Celine pack at most? (b). What was the mass of pistachios left? Give your answer as a fraction as a fraction in its simplest form.

Let's break this problem down step by step.

(a) To find out how many bags of pistachios Celine packed at most, we need to calculate the number of bags she can fill with the remaining pistachios.

First, let's calculate how many pistachios Celine had left after Saturday: She had 35 kg of pistachios. On Saturday, she used 3/5 of the pistachios, which is (3/5) * 35 kg = 21 kg. So, she had 35 kg - 21 kg = 14 kg of pistachios left.

Now, on Sunday, she used 4/7 of the remaining pistachios. Let's calculate how many pistachios she used on Sunday:

Amount used on Sunday = (4/7) * 14 kg = 8 kg

Now, she had 14 kg - 8 kg = 6 kg of pistachios left.

Each bag contains 5/8 kg of pistachios.

Number of bags = (Amount of pistachios left) / (Amount per bag) Number of bags = (6 kg) / (5/8 kg/bag)

Now, divide to find the number of bags:

Number of bags = (6 kg) / (5/8 kg/bag) Number of bags = (6 kg) * (8/5 kg/bag) Number of bags = 48/5 bags

Since you can't have a fraction of a bag, you take the ceiling value of 48/5, which is 10 bags.

So, Celine can pack at most 10 bags of pistachios.

(b) To find the mass of pistachios left, it's 6 kg as calculated earlier. In terms of a fraction in its simplest form, you can represent this as 6/1, which is already in its simplest form.