Step 1 :Calculate the total hours worked by Blue from Monday to Saturday: \(12 + 9 + 9 + 9 + 9 + 3 = 51\) hours.
Step 2 :Calculate the total regular hours and total overtime hours for Blue. The total regular hours are 40 hours and the total overtime hours are \(51 - 40 = 11\) hours.
Step 3 :Calculate the overtime rate. The overtime rate is a time-and-a-half rate, which means it's 1.5 times the regular rate. So, the overtime rate for Blue is \(1.5 * 8.00 = \$12.00\).
Step 4 :Calculate the gross earnings for Blue. The gross earnings are the sum of the earnings from the regular hours and the overtime hours. The earnings from the regular hours are \(40 * 8.00 = \$320.00\) and the earnings from the overtime hours are \(11 * 12.00 = \$132.00\).
Step 5 :Add the earnings from the regular hours and the earnings from the overtime hours to get the gross earnings for Blue: \(320.00 + 132.00 = \$452.00\).
Step 6 :\(\boxed{\text{So, the gross earnings for Blue are } \$452.00\)}