Question

A 25% orange juice drink is mixed with a 100% orange juice drink. The function f(x) = (4)(1.0)+z(0.25)

models the
4+z
concentration of orange juice in the drink after a gallons of the 25% drink are added to 4 gallons of pure juice.
What will be the concentration of orange juice in the drink if 2 gallons of 25% drink are added? Give the answer as a percent
but do not include the percent sign (%).

Answer 1

To solve the problem, we need to use the given function f(x) = 4 + z(0.25) where x is the amount of 25% orange juice drink added and z is the amount of 100% orange juice drink added.

We know that initially 4 gallons of pure juice are present. So, the total amount of juice in the mixture is 4 + x gallons.

When we add 2 gallons of 25% orange juice drink, x = 2 and z = 0. So, using the function f(x), we get:

f(2) = 4 + z(0.25)

= 4 + 0(0.25)

= 4

Therefore, the concentration of orange juice in the drink after adding 2 gallons of 25% orange juice drink is 4%, expressed as a percent but without the percent sign.

Answer: 4