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

240 marbles.

Step-by-step 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:

`(1)/(3)N=R`

Since N = R + 160, the above becomes

`(1)/(3)(R+160)=R`

Multiplying both sides by 3 gives

`3*(1)/(3)(R+160)=R*3`
`R+160=3R`

subtracting R from both sides gives

`R+160-R=3R-R`
`160=2R`

Finally, dividing both sides by 2 gives

`R=(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.