5. charlie works part - time at a local fast - food restaurant. on his next pay cheque, he will receive a 5%…

5. charlie works part - time at a local fast - food restaurant. on his next pay cheque, he will receive a 5% increase in pay on top of a 10% performance bonus. charlie tells his friends he is receiving a 15% raise in pay. is he correct? explain and include an example.

5. charlie works part - time at a local fast - food restaurant. on his next pay cheque, he will receive a 5% increase in pay on top of a 10% performance bonus. charlie tells his friends he is receiving a 15% raise in pay. is he correct? explain and include an example.

Answer

Explanation:

Step1: Assume original pay

Let the original pay be $x$.

Step2: Calculate pay after performance - bonus

The pay after a 10% performance - bonus is $x(1 + 0.1)=1.1x$.

Step3: Calculate pay after 5% increase

The pay after a 5% increase on the already - bonus pay is $1.1x(1 + 0.05)=1.1x\times1.05 = 1.155x$. The overall raise is $\frac{1.155x−x}{x}\times100%=15.5%$, not 15%.

Answer:

No, Charlie is not correct. For example, if his original pay $x = 100$, after a 10% performance - bonus, his pay is $100\times(1 + 0.1)=110$. Then, after a 5% increase on this amount, his pay is $110\times(1 + 0.05)=115.5$. The overall raise is $\frac{115.5 - 100}{100}\times100%=15.5%$.