Hector has a part-time job at a garage. He gets a paycheck of $\$820$ every four weeks.  

1. Hector has to pay $15\%$ of his income in taxes. How much money does he pay in taxes each paycheck? Show your thinking with a diagram and calculations.

   Hint (a):

   

   More Help (a):

   $(0.15)(820)$

   Answer (a):

   $\$123$

2. Hector took a $1$-week vacation, so his next paycheck will only be for $3$ weeks of work. What percentage of his regular pay should he expect to receive? How much is that?

   Hint (b):

   $3$ weeks is what percent of $4$ weeks?

3. The garage owner is impressed with Hector’s work and is giving him a $10\%$ raise. How much will Hector be paid when he receives his next $4$-week paycheck?

   Hint (c):

   Find $10\%$ of Hector's current paycheck.

   More Help (c):

   Add this amount to his current paycheck to find the amount of his new paycheck.

   Answer (c):

   $\$902$