Mathematical and Physical Journal
for High Schools
Issued by the MATFUND Foundation
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Problem C. 870. (November 2006)

C. 870. A car dealer sold 7 cars per day on the average in a certain period. If the day of the smallest number of cars sold is not counted, the average number of cars sold per day will be 8. If the day of the largest number of cars sold is not counted, the average will be 5. Finally, if both of these days are ignored them, the average will be 5.75 cars per day. What was the total number of cars sold by the dealer in the given period?

(5 pont)

Deadline expired on December 15, 2006.


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

Megoldás. A szóban forgó időszak álljon k napból, a leggyengébb napon eladott autók számát jelölje g, a legerősebb napon eladottakét e. Ekkor:

(1)\frac{7k-g}{k-1}=8,\qquad{\rm amib\H ol}\qquad 7k-g=8k-8,
(2)\frac{7k-e}{k-1}=5,\qquad{\rm amib\H ol}\qquad 7k-e=5k-5,
(3)\frac{7k-g-e}{k-2}=5,75,\qquad{\rm amib\H ol}\qquad 7k-g-e=5,75k-11,5.

(1) és (2) összegéből kivonva (3)-at azt kapjuk, hogy 7k=7,25k-1,5, amiből k=6, és így az eladott autók száma 7k=42.


Statistics:

490 students sent a solution.
5 points:448 students.
4 points:7 students.
3 points:10 students.
2 points:10 students.
1 point:2 students.
0 point:6 students.
Unfair, not evaluated:7 solutions.

Problems in Mathematics of KöMaL, November 2006