Answer
$Mass\space of\space the\space balloon= 68.36\space kg$
$Mass\space of\space the\space basket= 7.23\space kg$
Work Step by Step
Please see the image first.
Let's apply equation $F=ma$ to the balloon.
$\uparrow F=ma$
Let's plug known values into this equation
$688\space N-m_{1}g=m_{1}\times0.265\space m/s^{2}$
$688\space kgm/s^{2}= (0.265+9.8)m_{1}\space m/s^{2}$
$68.36\space kg=m_{1}$
Let's apply equation $F=ma$ to the basket.
$\uparrow F=ma$
Let's plug known values into this equation
$72.8\space N-m_{2}g=m_{2}\times0.265\space m/s^{2}$
$72.8\space kgm/s^{2}= (0.265+9.8)m_{2}\space m/s^{2}$
$7.23\space kg=m_{2}$
$Mass\space of\space the\space balloon= 68.36\space kg$
$Mass\space of\space the\space basket= 7.23\space kg$
