Question

an employee at a health food company is making a new type of trail mix. she starts with 10 lbs of hearty mix, which contains 25% dried fruit by weight. she then adds x lbs of active mix, which contains 40% dried fruit by weight. let y be the percent of dried fruit in the new type of trail mix. which function models situation? y = (0.25 + 0.4x)/(10 + x) · 100; y = 0.65/(10 + x) · 100; y = (2.5 + 0.4x)/(10 + x) · 100; y = (0.65x)/(10 + x) · 100

Explanation:

Step1: Calculate dried fruit in Hearty Mix

The Hearty Mix is 10 lbs with 25% dried fruit. So dried fruit from Hearty Mix is $10\times0.25 = 2.5$ lbs.

Step2: Calculate dried fruit in Active Mix

The Active Mix is $x$ lbs with 40% dried fruit. So dried fruit from Active Mix is $x\times0.4 = 0.4x$ lbs.

Step3: Total dried fruit and total weight

Total dried fruit is $2.5 + 0.4x$ lbs. Total weight of the new mix is $10 + x$ lbs.

Step4: Calculate percentage of dried fruit

The percentage $y$ is (total dried fruit / total weight) $\times 100$, so $y=\frac{2.5 + 0.4x}{10 + x}\times100$.

Answer:

$y=\frac{2.5 + 0.4x}{10 + x}\times100$ (the third option)