Sometimes, deduction rates can be tricky. The tutor offers an example of a “circular argument.”

Let’s imagine a benevolent employer offers a health plan that costs 6% of the employee’s net income. The company’s definition of net income is gross pay minus the health plan deduction. Find the monthly health premium of an employee whose gross monthly pay is 2500.

Solution:

Let p be the premium amount.

p=0.06(2500 – p)

Expanding, we get

p=150 – 0.06p

Adding 0.06p to both sides, we get

1.06p=150

Dividing both sides by 1.06, we arrive at

p=150/1.06

Finally, p=141.51

Apparently, the health premium for a gross income of 2500 is 141.51. Let’s check:

2500 – 141.51 = 2358.49

If our premium is correct, it should be 6% of 2358.49:

0.06(2358.49)=141.51

Algebra allows for circular arguments because the same variable can occur on both sides.

HTH:)

Jack of Oracle Tutoring by Jack and Diane, Campbell River, BC.