On a weekday, the shop produces 10 coffee cups per hour * 5 hours per weekday = <<10*5=50>>50 coffee cups.
The coffee shop therefore brewed 50 coffee cups per day * 5 weekdays in a week = <<50*5=250>>250 coffee cups.
So in total, the coffee shop brewed a total of 250 weekday coffee cups + 120 weekend coffee cups = <<250+120=370>>370 coffee cups in 1 week.
#### 370