KöMaL 2006 K77

The Silly family bought a tape measure that can be hung on the wall for measuring heights of people. One end of the tape reads 80 cm'' and the other end reads 180 cm'' (If he person to be measured stands on the floor, the tape can measure heights between 80 and 180 cm if properly used.) The Sillies hung the tape in a vertical position, but its lower end was not fixed at the appropriate height.To make it even worse, it also turned out that even the centimetre scale on the tape was wrong: the divisions of were not actually 1 cm apart. Thus the head of the 130-cm-tall Pete reached up to the 120-cm mark while the tape read 145 cm for his 150-cm-tall sister. What is the maximum height of a person that can be measured with this measuring tape with improper scale hung improperly on the wall?