# Problem of the Week Problem D Dye Refresher

To create an ink refresher for dye-based ink, some crafters will mix pure vegetable glycerine with water to get a mixture that is $$12\%$$ vegetable glycerine, by volume. Kathy does not have pure vegetable glycerine, but she does have

• a $$90$$ mL mixture that is $$10.5\%$$ vegetable glycerine,

• a $$120$$ mL mixture that is $$30\%$$ vegetable glycerine, and

• a $$1$$ L mixture that is $$7.5\%$$ vegetable glycerine.

Since Kathy is a math teacher, she knows she can use the contents of these three mixtures to create a mixture that is $$12\%$$ vegetable glycerine, by volume. She combines the contents of the entire $$90$$ mL mixture with the contents of the entire $$120$$ mL mixture, and then adds some of the $$1$$ L mixture. How many millilitres of the $$1$$ L mixture should she add to create a new mixture that is $$12\%$$ vegetable glycerine, by volume?