Mathematical and Physical Journal
for High Schools
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Problem K. 261. (October 2010)

K. 261. There are four numbers listed on a sheet of paper. The mean of the first two, the last two, and the middle two is 7, 8.4, and 2.3, respectively. What is the mean of the first and last numbers?

(6 pont)

Deadline expired on November 10, 2010.

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

Megoldás. Legyen a négy szám (sorrendben) \(\displaystyle a\), \(\displaystyle b\), \(\displaystyle c\) és \(\displaystyle d\). A feladat szerint az átlagok \(\displaystyle \frac{a+b}2=7\), \(\displaystyle \frac{c+d}2=8,4\), \(\displaystyle \frac{b+c}2=2,3\). Az első kettő összege \(\displaystyle 15,4= \frac{a+b}2+\frac{c+d}2=\frac{a+d}2+\frac{b+c}2=\frac{a+d}2+2,3\), ahonnan \(\displaystyle \frac{a+d}2=13,1\). Az első és az utolsó szám átlaga 13,1.


358 students sent a solution.
6 points:287 students.
5 points:16 students.
4 points:8 students.
3 points:4 students.
2 points:22 students.
1 point:2 students.
0 point:6 students.
Unfair, not evaluated:13 solutionss.

Problems in Mathematics of KöMaL, October 2010