Create scale (or index) using items that are measured on with different scales


I would like to make a scale of several items that are theoretically related, have a >.8 cronbach's alpha, but were measured on different scales themselves. Also, each factor has a different number of items. So,

questions 1~3 measured by 1 = very small ~ 5 = very large

questions 4~5 measured by 1 = Not at all necessary ~ 5 = highly necessary


questions 6~10 measured by 1 = no influence ~ 10 = great influence

Note that questions 6~10 not only use a different scale (values), they also use a different range (1~10 rather than 1~5).

Can I create the combined scale in the following way?

1. Save the standardized (Z) scores of all the items
2. Add all of the Z scores together and divide by the number of items (the mean of the scores)?

In proceeding this way, will any extra weight be given to, say, questions 6~10 because there are more of then (4 questions in total)?