Solving Systems with Cramer's Rule · Exercise 67

Use this scenario: A health-conscious company decides to make a trail mix out of almonds, dried cranberries, and chocolate-covered cashews. The nutritional information for these items is shown in the table.
$$\begin{array}{cccc}& \text{Fat (g)}& \text{Protein (g)}& \text{Carbohydrates (g)}\\ \text{Almonds (10)}& \text{6}& \text{2}& \text{3}\\ \text{Cranberries (10)}& \text{0.02}& \text{0}& \text{8}\\ \text{Cashews (10)}& \text{7}& \text{3.5}& \text{5.5}\end{array}$$

For the “hiking” mix, there are 1,000 pieces in the mix, containing 390.8 g of fat, and 165 g of protein. If there is the same amount of almonds as cashews, how many of each item is in the trail mix?

OpenStax, Algebra and Trigonometry 2e · §11.8 Solving Systems with Cramer's Rule · Exercise 67