Sum columns based on header cell

Hello,

I am a teacher and use excel to do grades. One of the sheets I made contains a column for every grade for the semester. Grades are weighted and assigned per weighting category. What I want to do is sum each category grade into one column. There can be a total of 10 categories and the categories are arranged by date which means I need a formula that looks up each column based on the category and adds them together. There is also one more obstacle. If a student is excused from the assignment there is an "x" instead of a score. I need this to not affect the calculation. Does anyone know how I can do this? I have attached a sample worksheet. B4:U63 are the scores and I need the formula in Z4:AJ63.

Thanks for any help.