Mathematical and Physical Journal
for High Schools
Issued by the MATFUND Foundation
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Problem C. 961. (November 2008)

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 pont)

Deadline expired on December 15, 2008.


Sorry, the solution is available only in Hungarian. Google translation

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:

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