Every student at Darcy School is in at least one of three clubs: horseback riding, embroidery, and country dancing,

Every student at Darcy School is in at least one of three clubs: horseback riding, embroidery, and country dancing, which are the only clubs in existence at the school. The ratio of the number of students in exactly two clubs to the number of students in exactly one club is $4{:}3,$ while the ratio of the number of students in exactly two clubs to the number of students in at least two clubs is $5{:}7.$ Which of the following could be the total number of students at Darcy School?

A. $63$
B. $69$
C. $74$
D. $82$
E. $86$

The OA is E

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