In a bag,there are 18 cards of which x cards are coloured and the rest are white.When another 6 white cards are added into the bag,the probability of a white card being picked is x over 8.Find the value of x.

Question

In a bag,there are 18 cards of which x cards are coloured and the rest are white.When another 6 white cards are added into the bag,the probability of a white card being picked is x over 8.Find the value of x.

Answer:6

How?

Answer 1

now: x and 18-x

after 6 more whites: x and 24-x

(24-x)/24 = x/8
8(24-x) = 24x
192-8x = 24x
32x = 192
x = 6

Answer 2

To find the value of x, we can set up an equation based on the given information.

Let's break down the problem:
- Initially, there are 18 cards in the bag, with x colored cards and the rest (18 - x) white cards.
- After adding 6 more white cards, the total number of cards in the bag becomes (18 + 6) = 24.

According to the question, the probability of picking a white card from the bag is x/8.

We can set up the equation as follows:
(x/24) = (x/8)

Now, we can solve for x by cross-multiplying:
8 * x = 24 * x

Simplifying further, we have:
8x = 24x

To solve for x, we need to isolate it on one side of the equation. We can do this by subtracting 24x from both sides of the equation:
8x - 24x = 0

Simplifying:
-16x = 0

Now, divide both sides of the equation by -16 to obtain the value of x:
x = 0/-16

Thus, x = 0.

However, this value of x does not make sense in the given context because at least some white cards need to be present in the bag initially. Therefore, x must have a positive value.

Let's try assuming that there are no colored cards initially, i.e., x = 0.

In this case, the number of white cards is (18 - x) = (18 - 0) = 18.
After adding 6 more white cards, the total number of white cards in the bag becomes (18 + 6) = 24.

Now, let's calculate the probability of picking a white card from the bag:
Probability = Number of favorable outcomes / Total number of outcomes
= 24 (number of white cards) / 24 (total number of cards)

Simplifying:
Probability = 24/24 = 1

But we are given that the probability of picking a white card is x/8. Since x = 0 in this case, the probability is 0/8 = 0.

So, assuming x = 0 does not satisfy the given condition.

Therefore, x = 6 is the correct value that satisfies the condition.