Answer :
To determine the cost of the dress:
Let the cost of the dress = C
Let the cindy's savings = x
Let the kendra savings = y
Kendra has $30 more savings than Cindy
[tex]y=30+x\ldots..\text{. }(1)[/tex]The dress cost = 2/3 of cindy's savings and = 1/2 of kendra's savings
[tex]\begin{gathered} C=\frac{2}{3}x=\frac{1}{2}y \\ \frac{2}{3}x=\frac{1}{2}y \\ \text{cross multiply} \\ 4x=3y \\ 4x-3y=0\ldots\ldots(2) \end{gathered}[/tex]substitute y in equation (2)
[tex]\begin{gathered} 4x-3y=0 \\ 4x-3(30+x)=0 \\ 4x-90-3x=0 \\ 4x-3x=0+90 \\ x=90 \end{gathered}[/tex]Cost of the dress = 2/3 of cindy's
[tex]C=\frac{2}{3}x=\frac{2}{3}(90)=\text{ \$60}[/tex]Therefore the cost of the dress = $60