[ Percentage and Ratio Problems ]

Karlson ate $40 \%$ of the cake for breakfast, and Little One ate 150 g. For lunch, Fräulein Bock ate $30 \%$ of the remainder and another 120 g, and Matilda licked the remaining 90 g of crumbs from the cake. What was the initial weight of the cake?

#
$90+120=210$ g remained after Freken Bok ate $30 \%$ of the remainder. Since Freken Bok ate $30 \%$ of the remainder, 210 g is $70 \%$ of the remainder.

$210: 0.7=300$ g was before Freken Bok started her lunch. $300+150=450$ g was before Little Man started eating. Since Karlson ate $40 \%$ of the cake, 450 g is $60 \%$ of the cake.

$450: 0.6=750$ g - the initial mass of the cake.

## Answer

750 g.