



 
Yes. The units can be though of as "perdollars" or $ \$^{1}.$ Multiplying a number with such a dimension by a number with the dimension "dollars" yields a dimensionless number. So for instance if we are told that $35$ unspecified items cost $\$5,$ we can perform the calculation you describe above to determine that the items are seven per dollar. To find out how many you get for $ \$3,$ multiply $(\$3)\times(7 \$^{1} )$ to get a dimensionless $21$ as your answer. Good Hunting!  


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