Algebra and mathematics

Question

if a range hood removes contaminants at a flow rate of F liters of air per second then the percent P of contaminants that are also removed from the surrounding air can be modeled by P = 1.06F + 12.12 where F is between and inclusive of 25 and 75. what are the minimum and maximum values for P in this model?

Answer 1

Hi Ronnie, this one only looks tough:

if a range hood removes contaminants at a flow rate of F liters of air per second then the percent P of contaminants that are also removed from the surrounding air can be modeled by P = 1.06F + 12.12 where F is between and inclusive of 25 and 75. what are the minimum and maximum values for P in this model?

We have an equation to work with:

P = 1.06F + 12.12

We also have two values for F:

25

75

Substitution comes next:

P = 1.06 x 25 + 12.12 P = 1.06 x 75 + 12.12

P = 26.5 + 12.12 P = 79.5 + 12.12

P = 38.62% (min) P = 91.62% (max)

See? Not so bad.

Answer 2

P = 1.06 F + 12.12

P - 12.12 = 1.06F

(P - 12.12) / 1.06 = F

25 < F < 65

25 < (P - 12.12) / 1.06 < 65

Can you slave for P and answer?