Any shipment of peanuts that contains more than 25 ppb of this dangerous fungus is rejected. A company receives 24 t of peanuts to make peanut butter. What is the maximum mass, in g, of fungus that is allowed? Hint 1 t = 1000 kg.

0.60g of the fungus can be allowed

Explanation:

The maximum concentration of the fungus that can be allowed is 25 ppb, that is 25mg/t.

As the peanuts are 24t, the mass of fungus that can be allowed is:

24t * (25mg/t) = 600mg of the fungus can be allowed. In grams are:

600mg * (1g/1000mg) =

0.5g of toxin

Explanation:

ppb = mass of solute/ mass of solution x 10^9

ppb = mass of fungus/ mass of peanuts x 10^9

25ppb = (x/2 x 10^7g) x 10^9

x = (25)(2 x 10^7g)/ 10^9

x = 0.5g of toxin

x represented the unknown mass of solute (fungus), in which we solved for. We already knew we were using the ppb formula, which is mass of solute/ mass of solution x 10^9, because the question mentions that there are 25ppb of peanuts in the shipments. In the calculations, you can see that I substituted the mass of peanuts with 2 x 10^7g. I did this because the question mentions that there are 20t of peanuts and since each t = 1000kg, I multiped 20 x 1000 to get 20 000kg. In my formula for ppb, I know that I have to use grams of solution, not kilograms. Knowing this, we follow the formula for ppb and substitute our known values and solving for unknown values.