How do I solve this problem?

Question

If a hood range 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=1.16F+31.23, where F is between and inclusive of 10 and 75. What flow rate F must a range hood have to remove 83% of the contaminants from the air?

Answer 1

You want to remove 83% of the contaminants, so let P = 83.

Solve for 1.16F + 31,23 = 83, and if that answer is from 10 to 75, then your range hood can do the job.

1.16F + 31.23 = 83

Subtract 31,23 from both sides

1.16F = 51.77

Divide both sides by 1.16

F = 51.77/1.16 = 44.63 liters/second

No need to go the appliance store for a new hood!

Hope that helps