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C. 961. During the first half of the year, the price of gas was raised three times. The percentage increases were 5%, 6% and 10%. Experts predicted a total rise by 1/3 of the price during the whole year. If they are right, what further percentage rise is to be expected this year?

(5 points)

Deadline expired on 15 December 2008.


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

Megoldás. Az év eleji gázárat x-szel, a még várható áremelést (százalékban) p-vel jelölve felírható a következő egyenlet:

x\cdot1,05\cdot1,06\cdot1,1\cdot \frac{100+p}{100}=x\cdot4/3.

Innen x>0 miatt \frac{100+p}{100}=\frac43\cdot(1,05\cdot1,06\cdot1,1)\approx1,0891 következik, ahonnan p=8,91. Vagyis 8,91%-os további áremelésre lehet számítani.


Statistics on problem C. 961.
414 students sent a solution.
5 points:305 students.
4 points:36 students.
3 points:21 students.
2 points:32 students.
1 point:1 student.
0 point:8 students.
Unfair, not evaluated:11 solutions.


  • Problems in Mathematics of KöMaL, November 2008

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