Question

An employee at a health food company is making a new type of trail mix. She starts with 10 lb of Hearty Mix, which contains 25% dried fruit by weight. She then adds x lb 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?

Answer 1

Answer:
`y=(2.5+0.4x)/(10+x) .100`

Explanation:

Initially, the the total quantity of the mixture = 10 lb

In which dried fruit = 25% of 10 lb = 2.5 lb

Since, according to the question, employee adds x lb of Active Mix, which contains 40% dried fruit by weight.

So, the total mixture after addition =( 10+ x ) lb

In which total dried fruit= 2.5 lb+ 40% of x= (2.5+ 0.4x) lb

So the percentage of the dried fruit in the new mixture =( quantity of dried fruit in the mixture/ total quantity ). 100

=
`(2.5 + 0.4x)/(10+x) .100`

Answer 2

The correct answer is the third choice. 25% of the 10 pounds is 2.5 pounds and to represent 40% of x pounds would be represented as 0.4x. Together this is the amount that is dried fruit.

This gets placed over the total weight of mix (10 + x), and then multiplied by 100 to create the percent that is represented.