Question

There are only red and blue marbles in a box. The probability of choosing a red marble in the box at random is one third. If there are 160 blue marbles, how many marbles are in the box?

Answer 1

Answer:

240 marbles.

Explanation:

Let us call R the number of red marbles, B the number of blue marbles, and N the total number of marbles. Then we know that

$R+B=N$

Furthermore, we also know that there are 160 blue marbles, meaning B = 160:

$R+160=N$

We also know that the probability of getting a red marble is 1 / 3, meaning 1 /3 of the total number of marbles is red:

$\frac{1}{3}N=R$

Since N = R + 160, the above becomes

$\frac{1}{3}(R+160)=R$

Multiplying both sides by 3 gives

$3\times\frac{1}{3}(R+160)=R\times3$$R+160=3R$

subtracting R from both sides gives

$R+160-R=3R-R$$160=2R$

Finally, dividing both sides by 2 gives

$R=\frac{160}{2}$$\boxed{R=80.}$

Hence, there are 80 marbles in the box.

Therefore, the total number of marbles in the box is

$\begin{gathered} R+B=N \\ 80+160=N \\ \end{gathered}$$\boxed{N=240.}$

The total number of marbles in the box is 240.