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K. 77. 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?

(6 points)

This problem is for grade 9 students only.

Deadline expired on 10 March 2006.

Google Translation (Sorry, the solution is published in Hungarian only.)

Megoldás: A Peti és nõvére közti valójában 20 cm-es különbség a skálán mérve 25 cm. Tehát a skálán mérve 5 cm valójában csak 4 cm, így a skála teljes hossza valójában csak 80 cm. A 130 cm-es magasság a skálán 40 cm-rel, tehát a valóságban 32 cm-rel van feljebb, mint a skála kezdõpontja (a 80 cm-es jel), ezért a skála alja 98 cm magasságban van a talajtól. Ennek megfelelõen a teteje 178 cm-re van a padlótól, így legfeljebb 178 cm-es emberek mérhetõk meg ezzel a mérõvel.

Statistics on problem K. 77.
 146 students sent a solution. 6 points: 112 students. 5 points: 7 students. 4 points: 9 students. 3 points: 10 students. 2 points: 4 students. 1 point: 1 student. 0 point: 1 student. Unfair, not evaluated: 2 solutions.

• Problems in Mathematics of KöMaL, February 2006

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