Question

A bag contains 25 tickets, each colored either red or yellow. Red tickets are worth $0.50, and yellow tickets are worth $5.00. If the expected value of a ticket drawn at random from this bag is $3.20, how many of the tickets are red?

The answer to the question is 10, I just need an explanation why.

Answer 1

i would like one to. i came up with 6

Answer 2

10 red tickets

Step-by-step explanation:

Let us call x the number of red tickets.

Notice since there are 25 tickets in the bag then we have 25-x yellow tickets.

Now, the probability of drawing a red ticket would be:

`\displaystyle (x)/(25)`

And the probability of drawing a yellow ticket would be:

`\displaystyle (25-x)/(25)`

Then we multiply each probability by their values and sum up to get the expected value, so that we get the equation:

`\displaystyle 0.50\cdot(x)/(25)+5.00\cdot\displaystyle (25-x)/(25)=3.20`

We solve it like this:

Multiply both sides by 25 to clear of fractions:

`0.5x+5(25-x)=80`

Distribute:

`0.5x+125-5x=80`

Combine like terms:

`-4.5x+125=80`

Subtract 125 from both sides:

`-4.5x=-45`

Divide both sides by -4.5

`x=10`

There are 10 red tickets in the bag.