Mathematical and Physical Journal
for High Schools
Issued by the MATFUND Foundation
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Problem K. 576. (January 2018)

K. 576. A box contains some red and blue balls. If a ball is picked at random, the probability of its being blue is $\displaystyle \frac{2}{5}$. If one blue ball is removed from the box, the probability of a randomly selected ball being red will be $\displaystyle \frac{5}{8}$. How many balls are there in the box?

(6 pont)

Deadline expired on February 12, 2018.

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

Megoldás. A dobozban levő golyók $\displaystyle \frac25$ része kék. Jelölje a kékek számát $\displaystyle 2x$, a pirosak számát $\displaystyle 3x$. Egy kék golyót kivéve a piros húzásának valószínűsége $\displaystyle \frac{3x}{5x-1}=\frac58$. Innen rendezéssel kapjuk, hogy $\displaystyle 24x=25x-5$, amiből $\displaystyle x = 5$. Tehát a dobozban $\displaystyle 25$ golyó van ($\displaystyle 10$ kék és $\displaystyle 15$ piros).

Statistics:

 119 students sent a solution. 6 points: 105 students. 5 points: 3 students. 2 points: 3 students. 1 point: 4 students. 0 point: 4 students.

Problems in Mathematics of KöMaL, January 2018