Let ( r ) be the number of vases with red roses and ( p ) be the number of vases with pink roses. We know that ( r + p = 7 ) and the total number of roses is ( 6r + 12p = 66 ). Solving these equations, we first simplify the second equation to ( r + 2p = 11 ). Substituting ( p = 7 - r ) into this gives ( r + 2(7 - r) = 11 ), leading to ( r = 5 ). Thus, there are 5 vases with red roses.
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