B1. Frida bought herself a pair of pants that were $105 \mathrm{~cm}$ long. Since they were too long for her, she had a tailor shorten them by $5 \mathrm{~cm}$. After washing the pants and taking them out of the washing machine, she noticed that they were $2 \mathrm{~cm}$ too short. Of course, Frida had overlooked the attached sheet about shrinkage along the length.

a) What percentage of shrinkage did the manufacturer indicate?

b) To what shortest length should the tailor have shortened the pants (before washing) so that they would not be too short for Frida? Round the result to the nearest centimeter.
B1. The length of the shortened pants before washing was $105 \mathrm{~cm}-5 \mathrm{~cm}=100 \mathrm{~cm}$. After washing, they shrank by $2 \mathrm{~cm}$, which represents $2 \%$ of the length of the shortened pants before washing and is also the shrinkage percentage indicated by the manufacturer.

To have the shortened pants reach the desired length of $100 \mathrm{~cm}$ after washing, the tailor would have had to account for the $2 \%$ shrinkage indicated by the manufacturer before washing. This means that the length of $100 \mathrm{~cm}$ represents 98 \% of the shortest length to which the tailor Fridi should have shortened the pants. The shortest length is: $\frac{100 \cdot 100}{98}=102,04 \doteq 102 \mathrm{~cm}$.

## Scoring: Total: 5 points

a) Calculated shrinkage process: $2 \%$ ..... $1 \mathrm{p}$
Written answer, e.g.: The manufacturer indicated a shrinkage of $2 \%$. ..... $1 \mathrm{p}$
b) Calculated length to which the pants can still be cut: $102 \mathrm{~cm}$ ..... $2 \mathrm{p}$
Written answer, e.g.: The tailor can cut the pants to a maximum of $102 \mathrm{~cm}$. ..... $1 \mathrm{p}$