Exercise 47

There are red, yellow, and blue balls in a bag. The number of blue balls is half the number of red balls, and there are twice as many yellow balls as red balls. If there are 25 balls among the yellow and blue balls, then the number of blue balls is:

  1. 10

  2. 15

  3. 4

  4. 5

  5. 20

Try to solve it before checking the answer.

  1. 5

Let \( r\), \( a\), and \( m \) be the number of red, blue, and yellow balls, respectively. We have:

\( a = \cfrac{r}{2} \hspace{4em} \boldsymbol{(1)} \)

\( m = 2r \hspace{4em} \boldsymbol{(2)} \)

\( a + m = 25 \hspace{4em} \boldsymbol{(3)} \)

Replacing (1) and (2) in (3), we have:

\[ \begin{aligned} \frac{r}{2} + 2r = 25 &\Rightarrow r + 4r = 50 \\[.5em] &\Rightarrow 5r = 50 \\[.5em] &\Rightarrow r = 10 \\[.5em] &\Rightarrow a = \frac{10}{2} = \boldsymbol{5} \end{aligned} \]

That means there are 5 blue balls in the bag.

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