how to find an amount inclueded in my total pay

Question

I need to find the 4.4% bonus that my company includes with my final pay total.

 

There are three parts.

1. the total pay I earned ex. $500.00

2. the 4.4% amount from my pay that the company adds to my final pay: $500.00x4.4%=$22.00

3. the final total gross pay amount that I get: total $522.00

 

so I need to find out how to calculate the amount of part 2. (the $22.00) by only knowing parts 2 (not the $ but only the 4.4%) & 3

because I don't know the amount of part 1 but I do know that the 4.4% bonus of part 2 will always be the same.

 

thank you

Answer 1

Lets call the total gross pay T, and the base salary (which is unknown) x. 

 

Thus what we are given in part 2.) is .044x, and T must be the sum of of the unknown and part 2.)...so 

T=x+.044x = 1.044x.

 

Given the bonus amount and the total gross pay, we can divide their sum by 1.044 to find the base salary.

 

For your example observe that 522/1.044 = 500.

 

Hope that helps!

Answer 2

Hi James, you're definitely on the right track, you just need to construct an algebraic expression with the terms.

For example: 60% bonus with a gross amount of $800

x + x*0.60 = 800
x(1+0.60) = 800
x(1.60) = 800
x = 500

800 - 500 = $300 Bonus