Mary is $20\%$ older than Sally, and Sally is $40\%$ younger than Danielle. The sum of their ages is $23.2$ years. How old will Mary be on her next birthday?
$\mathrm{(A) \ } 7\qquad \mathrm{(B) \ } 8\qquad \mathrm{(C) \ } 9\qquad \mathrm{(D) \ } 10\qquad \mathrm{(E) \ }  11$
Let $m$ be Mary's age, let $s$ be Sally's age, and let $d$ be Danielle's age.  We have $s=.6d$, and $m=1.2s=1.2(.6d)=.72d$.  The sum of their ages is $m+s+d=.72d+.6d+d=2.32d$.  Therefore, $2.32d=23.2$, and $d=10$.  Then $m=.72(10)=7.2$.  Mary will be $8$ on her next birthday.  The answer is $\mathrm{(B)}$.