How to change mixture for a solution with a given ratio?

Question

I have a mixture with 70% of one composite element and 30% of another composite element.

I want to change the mixture to 50%/50% and the total weight to be 1kg or 1,000g.

How much of the 30% composite element do I add to the already mixed 70/30 to get 1000g? I know I can add 400g to 1000g to get 50/50 but I have 1400g total, it needs to be 1000g and I can't waste any extra solution. What's the math equation I would use?

Thank you.

Answer 1

The final solution must contain 500 g of each. First, we calculate how much of a 70/30 solution will yield 500 g of the 70% element. 70% of x = 500 x =500/.7 = 714.29 g of the mixture will yield 500 g of the 70% element. Merely add 285.71 g of the 30% element will complete the final mixture.

To double check your math, the 30% element is 285.71 + .3 x (714.29) = 500g