Systems of Equations word problems

Question

How would I set up equations to solve: 9 lbs. of mixed nuts containing 55% peanuts were mixed with 6 lbs. of another kind of mixed nuts that contain 40% peanuts. What percent of the new mixture is peanuts?

Answer 1

No equation in there, this is just a weighted average of two values (two percentages):

$$ New\space percentage = \frac{Sum\space of(weight\times percentage)}{Sum\space of\space weights} $$

Applied here, it becomes:

$$ New\space percentage = \frac{9\times 55 + 6 \times 40}{9 + 6} $$$$ New\space percentage = 49.4 \% $$

Answer 2

Hint: I wouldn't really do equations, just calculate. How many pounds of peanuts are in each part? How many total pounds of peanuts do you have? You have $15$ pounds of total nuts, so what is the percentage of peanuts in the total mix?