7.3. For breakfast, Karlson ate $40 \%$ of the cake, 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 mass of the cake?
Answer: 750 g.

Solution. First method (solving "from the end").

1) $90+120=210$ (g) of the cake remained after Fröken Bok ate $30\%$ of the remainder.

Since Fröken Bok ate $30\%$ of the remainder, 210 g is $70\%$ of the remainder.
2) $210 \div 0.7 = 300$ (g) of the cake was left before Fröken Bok started her lunch.
3) $300 + 150 = 450$ (g) of the cake was left before Little Man started eating.

Since Karlson ate $40\%$ of the cake, 450 g is $60\%$ of the cake.
4) $450 \div 0.6 = 750$ (g) is the initial mass of the cake.

Second method (formulating an equation). Let $x$ g be the initial mass of the cake, then after Karlson and Little Man's breakfast, $0.6x - 150$ (g) remained, and after Fröken Bok's lunch, $0.7(0.6x - 150) - 120 = 0.42x - 225$ (g) remained, which is 90 g licked by Matilda. We get the equation $0.42x - 225 = 90$, the solution to which is $x = 750$.

## Grading Criteria:

+ A complete and well-reasoned solution is provided

$\pm$ A solution "from the end" is provided, all actions are correctly performed and the correct answer is obtained, but explanations are missing

$\pm$ An equation is correctly formulated and solved, but explanations for formulating the equation are missing

$\mp$ An equation is correctly formulated, but it is not solved or an arithmetic error is made in solving it

$\pm$ The idea of solving "from the end" is present and at least the first action is performed correctly, but the solution is not completed or is completed with errors

$\mp$ Only the correct answer is provided (possibly with a check that it is valid)

- The problem is not solved or is solved incorrectly